Preheat the oven to 450˚ F. Line a baking sheet with foil. Toss the potatoes, bell pepper, onion, vegetable oil, 2 teaspoons salt, a few grinds of pepper, the paprika, garlic powder and thyme on the baking sheet and spread out. Bake, stirring once, until the vegetables are browned around the edges and tender, 40 to 50 minutes. Push the potatoes to one side of the baking sheet so that they cover about half the pan.
Make a 6-by-9-inch tray out of a double layer of foil; the sides should be about 1 1/2 inches high. Place the foil tray in a corner of the baking sheet and coat with cooking spray. Whisk the eggs, cheese, milk, 2 scallions, 1 teaspoon salt and a few grinds of pepper in a large bowl. Pour the egg mixture into the foil tray. Arrange the sausage patties, overlapping if necessary, in the remaining space on the pan.
Return the pan to the oven and bake until the omelet is puffed and set and the sausages are heated through, 20 to 25 minutes. Let sit a few minutes before serving. Top the omelet with the tomatoes and herbs; sprinkle the sausage with the remaining sliced scallion.