Preheat the oven to 375 degrees F. Set aside a casserole dish.

Fill a medium-large pot about halfway with water. Bring to a boil, then add the cauliflower florets. Boil for 5 minutes, then use a slotted spoon to remove the cauliflower and set aside in a large bowl.

Add the sweetpotatoes to the same pot with the water, adding more if needed. Boil for 10 minutes, or until tender.

Drain sweetpotatoes and place them in a bowl of a mini food processor. Let cool for a few minutes, then puree until smooth, leaving the spout open on the food processor bowl.

In the same pot previously used, heat the butter over medium heat. Add the garlic and cook for a minute, until fragrant. Add the flour and cook for another minute, stirring often, until it starts to turn a light golden color.

Pour in the milk little by little, stirring after each addition, until all the milk has been added and is well combined.

Add the salt, paprika, pepper, nutmeg, and pureed sweetpotatoes. Reduce heat to medium-low and cook for 2-3 minutes, stirring often, until well combined.

Add ½ cup of the cheddar cheese and ¼ cup of the parmesan cheese to the sauce mixture. Cook for another 1-2 minutes, stirring often, until well combined.

Pour a layer of the cheese sauce in the bottom of the casserole dish. Take the bowl of cauliflower and dab it with paper towels to remove any excess moisture that is on the vegetables. Add the cauliflower to the casserole dish, then pour the remaining cheese sauce on top. Sprinkle with the remaining ½ cup of cheddar cheese, the remaining ¼ cup of parmesan cheese, and the breadcrumbs, then drizzle with the olive oil.

Bake at 375 degrees F for 25-35 minutes, until the mixture is bubbly and the breadcrumbs are golden brown on top. Let cool for at least 15 minutes for sauce to fully thicken, then serve warm and enjoy.