Open-Face Mushroom Sandwiches With Pecorino Salsa Verde

Six–eight 10" metal skewers or bamboo skewers, soaked (optional)
Toss shallots, vinegar, red pepper flakes, and black pepper in a small bowl to combine; lightly season with salt (the Pecorino will add some saltiness, so bear that in mind). Let sit 3 minutes.
Meanwhile, very thinly slice Pecorino into tiles with a knife (irregular pieces are okay).
Add Pecorino, herbs, and oil to pickled shallots and toss gently to combine. Taste and season with more salt if needed; set aside.
Prepare a grill for medium-high heat; clean grate. Working one at a time, set mushrooms on their sides and slice lengthwise ¼" thick to make 3–4 planks per mushroom, depending their size. If your mushrooms are particularly small or you are using crimini, slice ½" thick and thread onto skewers to keep them from falling through grate.
Using some of the oil, brush cut sides of mushrooms and transfer to a large bowl or arrange on a rimmed baking sheet if skewered. Lightly brush both sides of each slice of bread with remaining oil and transfer to a platter.
Press each slice of bread down across grate for even contact and grill until browned with some lightly charred spots, about 2 minutes per side. The goal is a crunchy exterior with a still chewy center. Transfer bread back to platter.
Brush grate to clean. If using a gas grill, turn heat down to medium. A charcoal grill should be at the tail end of medium-high and headed toward medium at this point, but wait a few minutes if needed. Grill mushrooms, turning halfway through and moving around as needed to avoid flare-ups, until golden all over with lightly charred edges, 6–8 minutes for small pieces and 8–10 minutes for large ones. Return to bowl (slide off of skewers if needed). Add Pecorino salsa verde and toss to combine. Spoon mushroom mixture over grilled bread.