Preheat the oven to 375 degrees F.
In a large pan on medium-high heat, add the oil. When the oil begins to swirl, add the beef, Worcestershire sauce, paprika, a pinch of salt and a few grinds of pepper. Cook until the meat is browned, 6 to 8 minutes. Stir in the tomato paste and saute for a few minutes to intensify the flavor. Add the stock and bring to a simmer. Season again and remove the mixture to a bowl with a slotted spoon, leaving the fat in the pan.
In the same pan, add the onions and cook until almost tender. Then add the carrots, zucchini, bell peppers, a pinch of salt and a few grinds of pepper. Cook, tossing, until the vegetables are tender but still a bit crunchy, 6 to 8 minutes. Remove from the heat.
In the bottom of a 13-by-9-inch casserole dish in this order, layer half of the beef mixture, pressing it down to level it, and then sprinkle half of the cheese evenly over the beef. Pour the remaining half of the beef over the cheese and press down to level as well. Add the vegetables, followed by the remaining cheese; press to level. Top with the tater tots in a neat row like little soldiers. Sprinkle the top with paprika and bake until the edges on the tots turn golden brown, 25 minutes.
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