Place a medium pot filled halfway with water on high heat Bring water to a boil then add in pasta. Cook according to package instructions. Drain and rinse, reserve 1/4 cup of cooking water to use in the sauce later on.
Set out two shallow bowls. Beat egg and milk in first bowl. Add flour to the second bowl. Start by placing one artichoke at a time in milk/egg mixture and then continue to coat with flour, making sure to cover the artichoke evenly. Set artichokes aside on a cookie sheet or large plate until all are dredged.
Heat olive oil in a large sauté pan over medium heat. Add artichokes making sure to leave enough space so you can turn them. Cook for approximately 3 minutes per side, or until nicely browned.
Add lemon juice, vegetable stock, white wine and capers (be careful when adding liquid because the pan will STEAM!) Cook for approximately 6-8 minutes, uncovered, until the sauce has thickened.
Take the reserved 1⁄4 cup of the reserved pasta cooking water and add to the sauce pan. Add the pasta to the saucepan, tossing well to combine. Cook for a minute more to marry flavors. Top with parmesan cheese if desired.