Cook pasta according to package directions until al dente. Save 1 cup of pasta water, drain and set aside.
Pat chicken breasts dry with paper towels, season with salt and pepper on all sides and cut into cubes.
In a large skillet over medium heat, heat olive oil until shimmering. Add chicken and cook until fully cooked and browned on all sides, 3-4 minutes per side. Do not overcrowd the pan. If need be, do this in two batches.
Transfer chicken to a platter and cover with foil.
In the same skillet, heat 1 tablespoon of olive oil and add onion and cook until softened, 6-8 minutes. Stir in garlic and cook for 30 seconds. If need be, use 1-2 tablespoons of reserved pasta water to help scrape the bits at the bottom of the pan.
Stir in sun-dried tomatoes and cook, stirring constantly, until warmed through or until lightly simmering, about 3 minutes.
Add heavy cream and Treasure Cave Mild Crumbled Blue Cheese and stir until the cheese is partially melted and sauce comes to a simmer. If it is too thick, use pasta water to thin it out a half-cup at a time.