Skillet Chicken Parmesan With Gnocchi | Umami

Ingredients

• 2 medium skinless, boneless chicken breasts (about 1 lb.), patted dry
• 4¼ tsp. Diamond Crystal or 2½ tsp. Morton kosher salt, divided
• ¼ cup all-purpose flour
• ¼ cup (or more) extra-virgin olive oil
• 8 garlic cloves, finely chopped
• ½ tsp. crushed red pepper flakes
• 1 28-oz. can whole peeled tomatoes
• 1½ tsp. sugar
• 1 17.5-oz. package shelf-stable potato gnocchi
• 2 oz. Parmesan, finely grated
• 8 oz. part-skim mozzarella, sliced ¼" thick
• Basil leaves (for serving; optional)