Prepare pasta separately.
Season diced chicken with salt and pepper.
Add olive oil to saucepan on medium-high heat; add diced chicken and sauté until browned on all sides, about 2–3 minutes, then remove chicken with slotted spoon.
Reduce heat to medium and add butter, onion, garlic, and a pinch of salt, black pepper, and crushed red pepper; sauté until caramelized and slightly nutty, about 1 minute.
Add tomato paste and minced sun-dried tomatoes and sauté until browned, about 1 minute; add vodka to pan and reduce by 1/3, about 30 seconds.
Add crushed San Marzano tomatoes, basil, oregano, heavy cream, 1/2 teaspoon salt, and1/2 teaspoon black pepper to pan and bring to a boil; return chicken to pan and simmer, about 8-10 minutes.
Toss cooked pasta in vodka sauce and topwith freshly grated Parmesan cheese; season to taste with salt and pepper.