Bring a large pot of water to a boil.
While the water comes up to a boil, heat a drizzle of EVOO in a small skillet over medium-high heat. Add the bacon and crisp, 5 minutes. Drain on a paper towel-lined plate and reserve.
Salt the boiling water and add the cauliflower florets. Cook for 4-5 minutes, then remove the cauliflower with a spider or strainer and run under cold running water to stop the cooking process. Reserve the cooked cauliflower in a colander and reserve the pot of boiling water.
Place a medium size pot over medium heat. Melt the butter and whisk in the flour. Cook for 1 minute, then whisk in the milk and season with salt, pepper and nutmeg. Cook for a couple of minutes more, until thickened.
Pre-heat the broiler.
Drop the pasta in the same boiling water you cooked the cauliflower in and cook until just shy of al dente.
While the pasta cooks, remove the sauce from the heat and add two thirds of the of shredded cheese and the horseradish, reserved bacon and chives. Stir to combine.
Drain the pasta over the cauliflower to reheat the florets with the hot boiling water. Place the pasta and florets in the hot pot and add the cheese sauce. Stir to combine.
Transfer to a baking dish and top with the remaining cheese. Place under the broiler to brown the top. Serve with a spinach salad alongside.