To make the filling for the pillows ("ravioli"), combine the spinach and goat cheese well and set aside.
Begin the pasta dough by mounding the flour in the center of a clean room temperature work surface like a large wooden cutting board. Create a crater in the center of the mound. Crack the first egg into the center of the crater and add 1/2 teaspoon of the olive oil. With a fork, gently begin to scramble the mixture within the confines of the crater, whilst integrating the flour from the sides of the crater as you carefully beat the egg. Once the first egg is mostly mixed in, shore up the sides of the mound again with flour, maintaining the crater shape. Repeat the process with the 2nd egg and 1/2 teaspoon of olive oil, and again with the 3rd egg and remaining 1/2 teaspoon of olive oil. Start kneading the dough with your palms, allowing the warmth of your hands to impart elasticity to the dough. Knead for a count of about 400 strokes or until you feel you have created a cohesive mass. Wrap the dough in plastic wrap and allow it to rest for about 30 minutes.
While the pasta is resting, begin the sauce: Combine the milk, onion, bay leaf, cloves, and nutmeg, if using, in a medium saucepan over medium heat. Spoon the melted butter into a separate heat resistant bowl and gradually whisk in the cornstarch, blending thoroughly, then whisk in the Comte cheese. When the milk is fairly hot, pour a small amount of it into the cornstarch/cheese mixture, stirring until the milk is thoroughly blended in. Return this to the remaining milk mixture, and simmer for 15 minutes, stirring frequently. Remove saucepan from heat, season sauce, to taste, with white pepper, and salt if needed. Remove and discard bay leaf and cloves. Immediately put a sheet of plastic wrap on top of the sauce to prevent a skin from forming.
Begin making the spinach/cheese pillows. Have a bowl of water handy to moisten and seal the dough. Divide the dough in thirds. (You will be working with 1/3 of the dough at a time - keeping the balance wrapped in plastic wrap to prevent it from drying out.) Divide your first third of the dough in half. Use a pasta machine to gradually roll down each of these sections, successively reducing the setting on the machine until it's at the thinnest setting and lay on your floured dough board. Spoon 1 teaspoon of the spinach cheese filling at 4-inch intervals on the pasta dough, and top each with a knob of Brie cheese. Dip your fingers into the bowl of water and moisten the area surrounding the spinach/cheese filling. Cover the filling with the other rolled out piece of dough and press gently around the filling to seal, being careful not to flatten the filling or tear the dough. Using a pizza cutter, begin to cut the filled dough into ravioli squares. Remove each ravioli to a floured surface, pressing the edges firmly as you do so. Cover the ravioli with a towel and set aside for 2 hours. Bring a large saucepan of water to a boil, add the ravioli and cook for 1 minute. Remove the ravioli with a slotted spoon, drain on a paper towel, and keep warm.
Reheat the sauce. Serve pillows with sauce spooned over and garnished with parsley.