Heat olive oil in a 12-inch skillet over medium-high heat. Add sausage and cook, breaking it up with a wooden spoon, until browned and cooked through, about 6-8 minutes. Transfer to a plate with a slotted spoon, leaving the fat in the pan.

Reduce heat to medium. Add garlic and red pepper flakes to the skillet and cook until fragrant, about 30 seconds, stirring constantly so the garlic doesn't burn.

Pour in heavy cream and chicken broth, scraping up any browned bits from the bottom of the pan. Simmer for 3-4 minutes until slightly thickened. Stir in Parmesan until melted and smooth.

Add spinach in handfuls, stirring until wilted, about 2 minutes. It will look like too much at first but cooks down dramatically.

Return sausage to the skillet. Add butter and lemon juice, stirring until the butter melts and everything is coated in sauce, about 1 minute. Taste and season with salt and black pepper. Serve immediately with extra Parmesan.