Season the chicken on both sides with salt, pepper, and paprika.
Heat a large skillet over medium-high. Add olive oil and 1 tablespoon butter. Sear chicken 4 to 5 minutes per side until golden and cooked through to 165°F (74°C). Transfer to a plate and tent loosely with foil.
Lower heat to medium. Add remaining 1 tablespoon butter and the garlic. Cook 30 seconds until fragrant, stirring so it does not brown.
Pour in chicken broth and scrape up browned bits. Simmer 2 minutes to reduce slightly.
Stir in heavy cream and parmesan. Simmer 2 to 3 minutes, stirring, until the sauce lightly thickens and looks glossy. Add lemon juice and any resting juices from the chicken. Taste and adjust salt and pepper.
Add spinach, if using, and cook 30 seconds until just wilted.
Return chicken to the pan and spoon sauce over it. Add spiralized zucchini and toss gently for 1 to 2 minutes over medium heat until just tender but still crisp.
Finish with parsley and red pepper flakes to taste. Serve hot with extra sauce spooned over each portion.
Notes
Pat chicken very dry for the best sear and flavor.
Reduce the sauce just until it coats a spoon; it thickens more off heat.
Cook zucchini at the end so it stays crisp-tender and not watery.
If the sauce gets too thick, whisk in a splash of warm broth.