Preheat the oven to 350 degrees F. Bring a large pot of salted water to a boil. Heat a large cast-iron skillet over very high heat.
Dredge the chicken breasts in the Blackening Spice Rub. Place in the cast-iron skillet. Blacken both sides of the chicken, 2 to 3 minutes per side.
Transfer the chicken to a baking sheet and place in the oven until the internal temperature of the chicken reaches 165 degrees F on an instant-read thermometer, about 10 minutes.
Remove from the oven and slice the chicken into strips on the bias.
In a large skillet over medium heat, heat the olive oil. Add the garlic and lightly brown it, 2 to 3 minutes. Stir in the wine. Pour in the heavy cream, bring to a simmer and cook until the sauce is reduced by half. Add the sun-dried tomatoes and chicken slices.
Meanwhile, cook the fettuccine al dente, according to the package directions. Drain.
When the cream sauce is at the desired consistency, stir in 1/2 cup of the Parmesan, the sea salt, pepper and pasta.
To serve, toss the pasta with the cream sauce and serve on large rimmed plates. Garnish with the green onions and the remaining 1/4 cup Parmesan.
Blackening Spice Rub:
Combine the garlic, black pepper, salt cumin, onion, cayenne pepper, Italian seasoning, paprika and chili powder in a small bowl. Store in an airtight container.