Mini Beef Wellingtons

Name: Mini Beef Wellingtons
Ingredients: 1/2 (14- to 16-ounce) package frozen puff pastry, preferably all-butter; 2 medium shallots; 2 cloves garlic; 1/4 bunch (about 20 sprigs) fresh thyme; 1 pound cremini mushrooms; 4 (5-ounce, 1 1/2-inch thick) filets mignons; 1 1/4 teaspoons kosher salt, divided; 1/2 teaspoon freshly ground black pepper; 2 tablespoons vegetable oil; 2 tablespoons unsalted butter; 8 cold slices prosciutto (about 7 ounces total); 1 large egg; All-purpose flour, for dusting; Flaky salt (optional)