Being a GM who loves cartography, architecture and drawing, I often have amazing (battle-)maps for my players whereabouts (cities, dungeons, rooms, a lighthouse, a long-forgotten overgrown jungle temple, whatever). I always spent quite some time and effort on these maps so naturally I feel inclined to use them during the game, but at the same time I don't want to give away too much detail all at once. Now I tried redrawing battle maps piece by piece on our battle grid map but that just results in the nice pre-made battle map not being used at all, and I tried cutting up maps or covering up parts of maps but that just feels clumsy. Can someone please tell me if there are any other helpful techniques that I am overlooking for sharing increased pieces of a (battle-)map?
If you are proud of the maps you made, then integrate them as physical items in the game world. Arrange for the player-characters to obtain a map of the location they are going to explore. When you do, you can put the map you drew on the table. And now that it's already there, you can also use it as a map for combat encounters.
But keep in mind that the map might not actually be accurate. While the player-characters explore it, they might discover that some details are quite different than they were represented on your map. To keep track of that, you might have a separate "corrected" version of the map behind your DM screen (this version should also contain reminders of hidden information like traps or enemies).
If you need to visualize these differences, you can either sketch the correction onto the map during play or overlay the updated map section with a cutout you prepared earlier.
I have a DM who faced similar problems. This is how we solved it.
We use a projector aimed from the ceiling to the table, which is connected to a laptop. He scans his maps and then uses the projector to display them. He can then freely cover the map by various means using the laptop. The part of the table used for the projections is covered with ordinary white paper. He often draws on it to show spell effects.
This method took a bit of effort to set up, but if you're willing to spend some time and money on it, it can be worth it. It's versitile, and you really don't need an expensive projector.
The downside is always having to play at the same table. The group becomes a bit stationary. For us this wasn't a problem because we always played at the same spot (my house).
Depending on your situation there is multiple ways that this can be handled.
I run with an online group, and we use software for mapping/etc. It is perfect because I can freely display the sections of map that they already know while hiding the sections they cannot. I will not link to any, as a quick google search of "D&D map maker" will give quite a few results.
Something I use more typically is to just give them a map without any enemy markings/etc. Basically a layout map that they could simply purchase in town/etc. I find this good for a couple reasons; money sink, good narrative/plot opportunities, and saves me the trouble of redrawing the map for them as they explore.
Another thing (more a combination of the two) is Google Drive. Simple create a google sheet and share access to the party. Draw maps that they have acquired (not to mention they can also be used for combat). This is typically better with online parties, or ones with easy access to laptops/etc during the game.
On a final note, as a preference point I always think it is better to just share the maps with the players regardless of method. Unless you have a group who are very interested in cartography, it just drags the game down and slows everyone. I would not recommend letting something like this slow the game down needlessly.