What 5e build can throw the most dice regularly?

Question

Background

A new player recently played D&D for the first time in my regular campaign. I created a character for the player to ease her into the game. Afterwards, we discussed what she liked and disliked about it and she said:

Throwing lots of dice to attack makes me feel powerful, I really like that.

Question

So I am trying to help her build a character for another campaign with the optimisation criteria: throws a lot of dice for their attacks. It doesn't matter if they are dice of the same or of different kinds (all d6 or d10 + d6 + ... ). The focus for this criteria is combat only.

What build of what race/class combination could achieve this the best?

Constraints

The campaign will start at L3 or L5 (DM is unclear as of now), and will last for 3 or 4 levels. Multiclassing is not allowed.

The 'many dice' should not be only in a nova or rarely used ability. It doesn't matter if its a caster, a melee attacker or whatever, just that you throw a lot of dice all the time, all throughout the adventure day.

A good answer has a build that is viable. It doesn't need to be CharOp levels of optimised, but it shouldn't be a burden on the party either. Therefore, self-inflicted disadvantage (as mentioned in comments) is not in the solution space, as well as similar self-harming methods, unless they actually improve the combat capabilities of the character.

An answer that clearly discusses how and when which number of dice are thrown is a plus.

Sources

An answer that uses only officially released WotC materials is preferred, but unearthed arcana is acceptable.

To make this information more explicit:

• Yes, the player explicitly asked to throw many dice often
• Yes, it should be for the benefit of the party, as suggested by 'not a burden for the party'

Answer 1

Monk: Way of the Shadow

The Way of Shadows Monk with a quarterstaff will have two rolls per melee attack, will roll a different kind of die for damage, can use flurry of blows rolls when Ki is available (die rolls for attack and damage). Deflect Missiles increases the number of rolls when ranged enemies are involved. At level 5 there's another attack. Roll again.

Presuming that you do not have a Rogue/Thief in the party, and the Monk takes a background that will offer Tools/Thieves Tools (such as Urchin) she'll have lots of chances to roll the dice by using stealth and lock picking rolls, as well as making climb checks when appropriate. As levels go up uses of Ki will offer other opportunities(though less dice intensive than the Way of Four Elements monk). By level 4, the reduced damage from a fall (Slow Fall) should entice the Monk to climb more often as it presents a lower cost for failure.

The higher Wisdom makes the monk a prime roller for Perception, if others use the Help action. (Assuming the party understands how beneficial that is). If you want to add party face to the duties of your monk (rather incongruous for a Shadow Monk IMO) consider a half elf way of shadows Monk built on a point buy(not an optimized party face but a useful one):

Str 8
Dex 15 (+1 racial)
Con 14
Int 8
Wis 15 (+1 racial)
Cha 10 (+2 racial)
Offers an initial set up of S 8 D 16 C 14 I 8 W 16 Ch 12

Make sure the Persuasion and/or Intimidation skills are chosen, to boost that modest +1 from Charisma with proficiency.

This monk need not be strong and need not be smart, but will roll the dice a lot. (Climbing checks with Acrobatics versus Athletics should keep things interesting if the adventure has plenty of climbs and chances to use acrobatics).

You could make the same Way of the Shadow Monk, almost, with a Ghostwise Halfling: Point buy: 8, 14(+2 racial dex) , 14, 8, 15(+1 racial wisdom), 12 =>
Str 8, Dex 16, Con 14, Int 8, Wis 16, Cha 12.
The added benefit of doing this, in terms of die rolls, is the Halfling's racial ability to re-roll any 1 on a 1d20. A bit more rolling on top of all of the rest of it. (Thanks to yinzanat for reminding me of this Sword Coast Adventurer's Guide racial choice for halflings).

Not a burden to the party: no serious material needs, no magic item needs (by level 6), nothing but sly contribution to the party's goals and plenty of action in combat.

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Full disclosure: my Way of Shadows monk "died" because that group broke up. :( Never got that level 6 Ki Empowered Strike. I have found that both this monk, and another one (way of the open hand) in a campaign that's on hold, get plenty of action and rolls at low levels.