In a food processor, blend one cup cooked white beans with virgin olive oil, 1/4 cup balsamic vinegar, grated Parmesan cheese, egg and parsley until smooth (about 1 minute). Remove to medium mixing bowl and stir in remaining cup of beans. Season to taste with salt and pepper.
Lay out 1 sheet of pasta and cut into 8 pieces, 3 1/2-inches by 3 1/2-inches. Place 1 1/2 tablespoons filling in center of each square and fold corner to corner to form triangle shaped pillow. Press edge firmly around to seal. Continue with all remaining pasta. Should yield 32 ravioli. These can be set aside on a baking tray in refrigerator for 6 hours, separated by a kitchen towel.
Bring 6 quarts water to boil in a large spaghetti pot and add 2 tablespoons salt. Drop ravioli into water and return to boil. Lower heat slightly and cook just below boiling for 3 minutes.
Meanwhile, place sweet butter in 10-inch to 12-inch saute pan and cook until foam subsides and butter begins to brown. Turn off heat and add remaining 1/4 cup balsamic vinegar (careful: it will spatter). Remove ravioli from cooking liquid with spider and place in pan with butter and vinegar. Toss over medium heat and sprinkle with remaining cheese and parsley. Divide among 4 plates and serve immediately.