Combine the eggs and grated cheese in a small bowl. Set aside.
Cook pasta until tender in a pot of boiling salted water. Drain, place in a large bowl, and add the egg and cheese mixture immediately.
In a large saute pan, warm the olive oil, garlic, and red pepper flakes over medium high heat, being careful not to burn the garlic. When the garlic is sizzling, add the Brussels sprouts and remaining 1/4 tsp of salt.
Cook, stirring occasionally, until the sprouts are soft but slightly firm (about 3 minutes.)
Add the Brussels sprouts to the pasta and toss thoroughly. Sprinkle with pepper. Taste and add more salt or cheese as needed. Serve hot and enjoy!