Preheat your oven to 375°F (190°C). Lightly grease a medium baking dish (about 8x8 inches or similar size) with the olive oil and set aside.
Bring a large pot of salted water to a boil. Add the broccoli florets and cauliflower florets and cook for 3–4 minutes, just until slightly tender but still crisp. Drain well and let them sit in the colander for a few minutes to release excess moisture.
While the vegetables drain, place a large skillet over medium heat. Add the Italian sausage and cook, breaking it up with a spatula, for about 6–8 minutes, until browned and cooked through. If there is excess grease, drain it off carefully.
Reduce the skillet heat to low and add the butter and minced garlic to the cooked sausage. Stir and cook for about 30–60 seconds, just until the garlic is fragrant but not browned.
Add the cream cheese to the skillet and stir until it begins to melt and coat the sausage. Pour in the heavy cream and continue stirring until the mixture is smooth and gently simmering.
Stir in 3/4 cup of the shredded sharp cheddar cheese and 1/4 cup of the grated Parmesan cheese until they melt into the sauce. Season with the sea salt, black pepper, dried Italian seasoning, and 1/4 teaspoon smoked paprika. Taste and adjust seasoning if needed.
Add the drained broccoli florets and cauliflower florets to the skillet with the sausage cheese sauce. Gently fold everything together until the vegetables are evenly coated and well combined.
Transfer the mixture to the prepared baking dish, spreading it out into an even layer with a spatula.
Sprinkle the remaining 1/4 cup grated Parmesan cheese and remaining 1/4 cup shredded cheddar cheese evenly over the top. If you like, dust a small pinch of extra smoked paprika over the surface for color.
Place the baking dish in the preheated oven and bake for 18–22 minutes, or until the top is bubbling and lightly golden around the edges.
If you prefer a deeper golden crust, switch the oven to broil for 1–2 additional minutes, watching closely so the cheese does not burn.
Remove the dish from the oven and let the Keto Broccoli and Cauliflower Au Gratin with Sausage rest for about 5–10 minutes before serving. This allows the sauce to thicken slightly and makes it easier to portion.