Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper, then dredge in flour, shaking off excess.
Cook chicken for 4-5 minutes per side until golden brown and cooked through (165°F). Transfer to a plate.
Reduce heat to medium-low, add remaining olive oil, shallots, and sauté for 1 minute. Add garlic and cook for 20 seconds.
Pour in white wine, scraping up browned bits. Add chicken broth and Italian seasoning. Simmer until reduced by two-thirds (about 10 minutes).
Stir in cornstarch mixture to thicken the sauce. Add spinach and cook until wilted.
Pour in heavy cream and stir in parmesan until melted and smooth. Return chicken to pan, spooning sauce over it.
Let sit for a minute to meld flavors, then serve.
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Notes
Store leftovers in an airtight container in the fridge for up to 3 days. Reheat gently to avoid curdling.