Cut 2 large boneless, skinless chicken breasts in half horizontally (also known as butterflying). Pat dry with paper towels. Season all over with 1 teaspoon of the kosher salt and 1/2 teaspoon black pepper.
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 1 tablespoon of the olive oil to the pan and repeat browning the remaining chicken. Transfer to the same plate.
Reduce the heat to medium. Add the remaining 1 tablespoon olive oil, if needed, and heat until shimmering. Add 1 diced small yellow onion and cook, stirring occasionally until softened, 2 to 3 minutes. Add 3 minced garlic cloves, 1/2 cup thinly sliced sun-dried tomatoes, and 2 teaspoons dried Italian seasoning. Cook until fragrant, 30 seconds to 1 minute. Add 5 ounces baby spinach a handful at a time. Cook, stirring regularly, until just wilted, 1 to 2 minutes.
Add 1 ounce grated Parmesan cheese, 1 1/4 cups heavy cream, and the remaining 1/2 teaspoon kosher salt. 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. Return the chicken and any accumulated juices on the plate to the pan and cook until the chicken is cooked through and registers at least 165ºF on an instant-read thermometer, 4 to 7 minutes.