Bring stock to a simmer in a large saucepan. Keep warm over low heat, but do not boil. Heat a dutch oven over medium heat. Add 2 tbsp butter to the pot; swirl to coat. (Everything from here will be added to this pot.) Add garlic; cook 2 minutes, stirring occasionally. Add the Arborio rice and salt, cook 1 minute, stirring frequently. Add 1/2 cup stock; cook 2 minutes or until the liquid is absorbed, stirring frequently. Stir in 2 1/2 cups stock, 1/2 cup wine, 1/2 cup at a time, stirring nearly constantly until each portion is absorbed before adding the next (about 20-25 minutes or until rice is tender). Remove pot from heat. Stir in butter, salt, pepper, and parsley. Add 2 eggs and put in the refrigerator while you make the pesto.