In a separate shallow dish, mix the 1 cup panko bread crumbs with 2 teaspoons thyme leaves, kosher salt, pepper, and 1 teaspoon olive oil. The oil helps the crust turn a nice golden brown in the oven. In another dish, beat the 2 eggs with 2 teaspoons water until the mixture is fluid.
Lightly dust each chicken roulade with the seasoned flour, then dip it into the egg mixture, letting any excess drip off. Finally, gently coat the chicken in the seasoned bread crumbs, pressing lightly to ensure an even crust. Carefully transfer the breaded roulades to a baking pan and bake for 20 minutes, until they are browned and cooked through, and the cheese inside is gooey.