Sprinkle both sides of the chicken breasts with the blackening seasoning, pressing lightly to adhere.
Heat the olive oil in a cast iron or large skillet over medium-high heat until shimmering.
Add the seasoned chicken and cook about 5 minutes per side, or until cooked through; remove from the pan and keep warm.
Reduce heat to medium and add the butter to the same skillet; sauté the minced garlic and sliced red bell pepper until the pepper starts to soften, about 2 minutes.
Pour in the heavy cream and bring to a gentle simmer; cook for about 5 minutes to slightly thicken.
Lower the heat to low and add the cream cheese and grated Parmesan plus the salt, black pepper, white pepper, and dried thyme; stir until the cheeses melt and the sauce is smooth.
Add the cooked, drained fettuccine to the skillet and toss thoroughly to coat the pasta in the sauce.
Divide the fettuccine among four plates, top each with a cooked chicken breast, and finish with additional grated Parmesan if desired.
