When you randomly find Beltrame, he will ask you to find three mushrooms. You keep mushrooms across runs, you don't need to find them all in a single run.
*** Spoiler - click to reveal ***One is found in a room with a hint that it grows in the dark. Destroy all torches and it will grow.
The second is found by clearing a room where a large mushroom NPC is found. The third will show a small mushroom sprout. Bomb it.
After you've found them, you'll soon randomly find Beltrame again, he'll say to meet him at the hub between rounds.