Boil pasta to al dente according to package instructions. Drain and set aside.
Heat a large skillet over medium heat and melt the butter with the olive oil. Add the onion cooking until softened, approximately 4-5 minutes. Stir in minced garlic, garlic powder and italian seasoning continuing to cook for 1 minute.
Whisk in chicken stock and half & half and bring to a boil. If it begins to boil too rapidly, turn the heat down a little. Simmer for about 5 minutes or until the sauce has reduced and thickened. Season with kosher salt and black pepper, to taste.
Stir in the chicken and cook for 3-4 minutes until heated through.
Remove from heat and stir in pesto and cheese. Add the pasta, tomatoes and stir to coat. **I recommend adding the cheese in small increments and mixing well with each addition, to avoid seizing and sticking together.
Garnish with fresh chopped basil and fresh cracked black pepper and serve immediately.