Heat oven to 425 degrees and cover a sheet pan with parchment paper.
Add potatoes and cauliflower to sheet pan. Drizzle 3 tablespoons of oil over them, season to taste with salt and pepper, and spread the vegetables evenly over sheet pan.
Place sausages on top, nestling them over or in between the vegetables.
Bake for 30 to 35 minutes, until sausages are cooked through, potatoes are soft and brown, and cauliflower is brown and crisp around the edges.
In a small bowl, combine mustard, honey, and remaining 1 tablespoon oil.
Garnish the cooked sausage and vegetables with chopped parsley. Serve with the honey-mustard sauce on the side.
