Whisk ½ cup all-purpose flour, 2 teaspoons paprika, 1 teaspoon onion powder, and 1 teaspoon garlic powder together in a shallow bowl or pie plate.

Cut 3 medium boneless, skinless chicken breasts in half horizontally so you have 6 pieces. For pieces thicker than ¼-inch, working with 2 pieces at a time, place in a large resealable plastic bag and pound to an even ¼-inch thickness with the flat side of a meat mallet or small saucepan. Pat dry with paper towels. Season all over with 1 teaspoon of the kosher salt and ¼ teaspoon black pepper. Working with 1 piece at a time, dredge the chicken in the flour, shaking off any excess. Reserve 1 tablespoon of the remaining flour mixture, then discard the remaining.

Heat 2 tablespoons of the olive oil in a large (12-inch) stainless steel or cast iron skillet over medium 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 might not be cooked through). Add the remaining 1 tablespoon olive oil to the skillet and repeat browning the remaining chicken. Transfer to the same plate.

Melt 2 tablespoons unsalted butter in the skillet. Add 1 thinly sliced large yellow onion and the remaining ½ teaspoon kosher salt and cook, stirring occasionally, until softened, 5 to 8 minutes. Stir in 2 minced garlic cloves and cook until fragrant, about 30 seconds. Add the reserved flour mixture and cook, stirring regularly, for 1 minute to cook the floury taste out.

Stir in 2 cups low-sodium chicken broth and scrape up any browned bits from the bottom of the skillet with a wooden spoon. Bring to a boil. Reduce the heat to maintain a simmer. Return the chicken and any accumulated juices to the skillet in a single layer. Simmer until the chicken is cooked through and registers at least 165ºF on an instant-read thermometer, 5 to 6 minutes. Taste the sauce and season with more kosher salt as needed.