Bring a large pot of water to a boil and cook the pasta as directed on the box.
While the water heats, add the butter to a medium saucepan over medium-high heat. Once melted, whisk in the flour until combined and bubbly. Slowly whisk in the heavy cream, bring to a boil, then reduce heat and simmer until thickened, stirring frequently, around 10 minutes. Add 3 cups of the asiago, and the 1/2 cup parmesan and stir until melted. Season with kosher salt and pepper to taste.
Heat a high-sided skillet over medium medium-high heat. Add the olive oil to the pan. Divide the chicken breast into four pieces. In a medium bowl, whisk together the eggs. In another medium bowl combine the panko crumbs, remaining 1 cup of asiago cheese, garlic powder, oregano, salt, and pepper. Dredge the chicken in the eggs, then in the bread crumb mixture. Add the chicken to the hot pan and gently fry, turning occasionally, until browned and the chicken reaches an internal temperature of 165 degrees, around 7 minutes.
Add a heaping pile of spaghetti to a plate, then top with the asiago cheese sauce and asiago chicken. Serve immediately.