Cook pasta in a pot of boiling salted water according to package directions, drain.
Combine bread crumbs and 2 Tablespoons parsley in shallow bowl.
Pound breasts between 2 sheets of plastic wrap with a meat mallet to 1/2" thickness and season with salt and pepper. Coat both sides with crumb mixture.
Heat reserved sundried tomato oil in a a sauté pan over medium-high heat. Arrange cutlets in pan; sauté until brown, 4 minutes per side. Transfer cutlets to a plate and tent with foil.
Melt butter in same pan. Add onions, tomato paste and garlic; cook until onions soften, about 2 minutes. Remove pan from heat.
Add vodka and return pan to heat; cook until reduced by half; 2-3 minutes. Add broth and sundried tomatoes and simmer 3 minutes.
Stir in cream and pepper flakes; reduce heat to medium-low and simmer 2 minutes. Add pasta, pecorino and remaining 4 Tablespoons parsley; season with salt and pepper. Divide pasta among 4 plates and top with cutlets.