Mushroom Ravioli with Sage Brown Butter

Ingredient:

• 2 cups (about 9 1/2 ounces.; 270 g) 00 flour or all-purpose flour, plus more for dough and work surface
• 1 teaspoon kosher salt
• 3 large eggs
• 2/3 cup dried porcini mushrooms (5/8 ounces), soaked in 1 1/2 cups boiling water for 20 minutes
• 2 tablespoons extra-virgin olive oil
• 2 cups sliced fresh mushrooms, such as cremini or shiitake (5 ounces)
• 1/2 teaspoon kosher salt, divided, plus more to taste
• 1/4 teaspoon black pepper
• 2 garlic cloves, finely chopped
• 1 1/2 teaspoons fresh thyme leaves
• 3 tablespoons dry sherry
• 2 tablespoons unsalted butter, cut into 2 pieces
• 1 teaspoon grated lemon zest
• 1/3 cup whole-milk ricotta cheese
• 2 tablespoons mascarpone cheese
• 1 ounce Parmesan cheese, grated (about 1/4 cup)
• 1/2 cup unsalted butter, cut into 8 pieces
• 12 fresh sage leaves
• 1 cup sliced fresh mushrooms, such as cremini or stemmed shiitake (2 1/2 ounces)