In a large, high-sided skillet, spread bacon and mushrooms in an even layer. Cook over medium heat, stirring occasionally until bacon is crisp and mushrooms are tender and browned (10 to 12 mins.) Scrape the bacon mixture onto a paper towel-lined plate.
Season chicken all over with 1 tsp. salt and 1/4 tsp pepper. In the same skillet over medium heat, heat oil. Working in batches, cook chicken, turning occasionally until golden brown and cooked through. Transfer the chicken to another plate.
In the same skillet over medium heat, cook garlic, stirring until fragrant and lightly golden. Add vinegar and bring to a boil, stirring occasionally until syrupy and reduced by half.
Add cream and broth and 1/2 tsp salt. Bring to a simmer, whisking until smooth. Continue to simmer over medium heat until slightly thickened.
Add spinach and parmesan and cook, stirring, until spinach is just wilted.
Return chicken, bacon, and mushrooms to skillet and cook, turning chicken to coat and heat through about 2 minutes more.
