Slice the chicken breast into thin strips on the bias.
Dredge the chicken strips in the blackened seasoning. Heat a large nonstick skillet over very high heat. Add 1 tablespoon oil to the pan, then add the chicken. Blacken by cooking 2 to 3 minutes on the first side without stirring. Flip the chicken pieces to blacken the other side until the chicken is cooked through, about 1 minute. Remove the chicken to a bowl and lower the heat to medium.
Add the remaining 2 tablespoons oil to the pan. Add the garlic and cook, stirring occasionally, until lightly caramelized. Add the sun-dried tomatoes and cooked chicken.
Deglaze the pan with white wine. Add the heavy cream, increase the heat to maintain a simmer and reduce the cream sauce by half.
Meanwhile, generously salt the boiling water. Add the pasta and cook according to the package instructions until al dente.
When the cream sauce is to the desired consistency, stir in 1/2 cup Parmesan, 1 teaspoon kosher salt and 1 teaspoon freshly ground black pepper.
Lift the cooked pasta straight from the boiling water into the pan with chicken and sauce. Turn to coat evenly.
Nest the pasta on large rimmed plates, pour sauce over pasta, and garnish with scallions, tomato and the remaining 1/4 cup Parmesan.