Cook Pasta Al Dente: Bring a large pot of salted water to a rolling boil. Add the bucatini and cook according to package instructions until just tender but still firm to the bite (al dente). Drain, reserving a small cup of pasta water, and set aside.
Brown the Sausage: While the pasta cooks, heat a large skillet over medium-high heat. Remove sausage from casing and crumble it into the pan. Cook, stirring occasionally, until browned and fully cooked through, about 8 to 10 minutes. Transfer cooked sausage to a plate lined with paper towels to drain excess fat.
Sauté Vegetables: In the same skillet, add olive oil. Toss in the chopped onion and diced red and yellow bell peppers. Cook over medium heat until the onions are translucent and peppers soften, about 7 to 8 minutes, stirring occasionally.
Create the Cream Sauce Base: Reduce heat to medium-low. Add butter to the skillet and let it melt completely. Stir in minced garlic and cook for 1 minute until fragrant. Sprinkle flour over the vegetables and garlic, stirring continuously to cook out the raw flour taste—about 1 minute.
Incorporate Cream and Mustard: Slowly pour in the heavy cream while stirring constantly to prevent lumps. Add Dijon mustard and continue stirring until the sauce thickens slightly, which should take about 1 to 2 minutes.
Combine Sausage and Spinach: Return the browned sausage to the skillet and mix well. Add the fresh baby spinach and stir until the spinach wilts evenly into the creamy sauce.
Finish with Pasta and Seasoning: Add a few tablespoons of reserved hot pasta water to the sauce to loosen it slightly. Then toss in the drained pasta, stirring gently until the noodles are fully coated with the sauce and the spinach is well incorporated. Season with salt and pepper to your taste.
Serve Immediately: Plate the pasta hot, optionally topped with freshly grated Parmesan cheese for an extra layer of savory flavor.