Heat olive oil in a large pot over medium heat. Add chopped onion and cook until translucent, about 4–5 minutes. Add minced garlic and cook until fragrant.
Add sliced mushrooms and increase heat to medium-high. Cook until mushrooms soften and release juices, about 5–7 minutes.
Pour in chicken broth and bring to a gentle boil. Scrape any browned bits from the bottom of the pot.
Stir in shredded rotisserie chicken. Reduce heat to a simmer and let warm through for about 10 minutes.
Lower the heat, then stir in heavy cream and spinach. Cook until leaves wilt, about 1–2 minutes.
Taste and season with salt and black pepper. If too thin, simmer uncovered to concentrate flavors or thicken with cornstarch slurry.
Ladle into bowls and serve warm.
Notes
Serve with a drizzle of olive oil or parsley. Pairs well with crusty bread or salad.