Lemony Mushroom and Frisee Toasts

Name: Lemony Mushroom and Frisee Toasts
Ingredients: 35 cremini mushrooms; 4 tablespoons olive oil, divided; 1 tablespoon salted butter; 2 garlic cloves, minced; 3 sprigs fresh thyme; 2 bunches frisee lettuce; 1/2 tablespoon Dijon mustard; zest and juice of 1/2 lemon; sea salt, freshly ground pepper; 1 loaf pain de mie, or 1 baguette; 20 thin slices Pecorino cheese