Mince 3 garlic cloves. Coarsely chop ½ cup drained oil-packed sun-dried tomatoes.

Working with 1 piece of chicken at a time, place 4 boneless, skinless chicken breasts in a large resealable bag and pound to an even ½-inch thickness. Pat the chicken dry with paper towels. Season all over with 1 teaspoon of the kosher salt.

Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat until shimmering. Add half of the chicken in a single layer and sear until browned, 3 to 5 minutes per side. Transfer to a large plate (the chicken will not be cooked through). Add the remaining 1 tablespoon of the olive oil to the skillet and repeat searing the remaining chicken. Transfer to the same plate.

Reduce the heat to medium. Add the 1 tablespoon sun-dried tomato oil and heat until shimmering. Add the garlic, sun-dried tomatoes, and ¼ teaspoon red pepper flakes. Cook until fragrant, about 30 seconds. Add 1 tablespoon tomato paste and cook, stirring occasionally, until darkened in color, 1 to 2 minutes.

Add ½ cup low-sodium chicken broth, ½ cup heavy cream, and the remaining ½ teaspoon kosher salt. Stir to combine. Bring to a simmer, scraping up any browned bits from the bottom of the pan with a wooden spoon. Reduce the heat to maintain a gentle simmer and cook until the sauce is slightly thickened, 2 to 4 minutes.

Return the chicken and any accumulated juices on the plate to the pan. Cook until the chicken is cooked through and registers at least 165ºF on an instant-read thermometer, 4 to 7 minutes. Meanwhile, pick the leaves from 2 fresh basil sprigs and coarsely chop until you have about 2 tablespoons.

Garnish the chicken with the basil.