Preheat oven to 350°F. Coat a 9-by-13-inch baking dish with cooking spray. Bring a large saucepan of water to boil over high heat. Add 12 ounces pasta; cook according to package directions for al dente, stirring occasionally, about 8 minutes. Remove from heat; stir in spinach until wilted. Drain the mixture well.

Meanwhile, heat 2 tablespoons oil in a large skillet over medium-high heat. Add onion and ½ teaspoon each salt and pepper; cook, stirring often, until softened, about 2 minutes. Add chicken; cook, stirring occasionally, until no longer pink on the outside, 3 to 4 minutes. Stir in 1 teaspoon garlic; cook, stirring constantly, until fragrant, about 1 minute.

Reduce heat to medium-low. Add 2 tablespoons flour; cook, stirring constantly, until the chicken is coated and the flour smells nutty, about 45 seconds. Add ½ cup wine, scraping the bottom of the pan to loosen browned bits; cook, stirring often, until most of the wine has evaporated and the chicken is coated, 1 to 2 minutes. Stir in 1¼ cups cream; bring just to a simmer over medium heat. Stir in the pasta mixture. Remove from heat.

Add ½ cup each Parmesan and cream cheese to the pasta mixture; stir to combine. Transfer to the prepared baking dish; top with the remaining ½ cup Parmesan and ⅛ teaspoon salt. Cover tightly with foil. Bake until warmed through and bubbling slightly around the edges, 15 to 20 minutes.