Sprinkle chicken with ¼ teaspoon pepper. Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add the chicken; cook until golden brown on both sides and an instant-read thermometer inserted into the thickest portion registers 165°F, 4 to 5 minutes per side. Transfer the chicken to a plate. Do not wipe the skillet clean.

Add shallots, garlic and the remaining 1 tablespoon oil to the skillet. Cook over medium heat, stirring constantly, until the shallot is translucent, 1 to 2 minutes. Sprinkle with 2 tablespoons flour; cook, stirring constantly, until fragrant, about 1 minute. Add ¼ cup wine; cook, undisturbed, until most of the liquid has evaporated, about 30 seconds. Whisking constantly, add ½ cup broth in a steady stream. Cook, whisking constantly, until the mixture thickens, 1 to 2 minutes.

Add spinach and artichokes; cook, stirring often, until the spinach is wilted, 2 to 3 minutes. Stir in ½ cup cream, ¼ cup cream cheese, ¼ teaspoon crushed red pepper (if using) and ⅛ teaspoon salt. Return the chicken to the pan and cook, stirring occasionally, until the cream cheese has melted, 2 to 3 minutes

Remove from heat. Add ¼ cup Parmesan and 2 tablespoons basil; stir until the Parmesan is melted, about 1 minute. Garnish with pepper, if desired.