Add potatoes, 1 tbs salt, and enough water to cover the potatoes to a large pot. Bring to a boil over high heat and reduce to a simmer and cook until tender, about 20 minutes.
Drain the potatoes and return to the pot. Turn pot on low heat and let potatoes rest until they stop steaming, about 5 minutes.
Turn off the heat and mash the potatoes to get ride of big lumps.
While the potatoes are still hot, add the melted butter and heavy cream. Mix until smooth.
Meanwhile, preheat the oven to 425 F. While the potatoes are cooking, prepare the filling.
Heat a large, oven-safe skillet or Dutch Oven over medium-high heat. Brown and crumble meat for 3-4 minutes. Add salt and pepper to taste.
Add chopped onion and carrot and cook for 5 minutes, stirring occasionally.
Sprinkle flour into skillet, tossing to coat and mix in, then cook for about 1 minute.
Add tomato paste, broth, Worcestershire sauce, rosemary, and thyme, then stir to combine. Bring to a boil then reduce heat to let simmer on low until the sauce thickens slightly, about 10 minutes.
Stir in corn and peas to the mixture and remove from heat.
If using an oven-safe skillet, top the mixture in the pan with the mashed potatoes. If not, transfer to a baking dish before topping with the mashed potatoes. Garnish with paprika.
Place baking dish on a rimmed baking sheet (to catch any drippings) and bake until potatoes are browned, 10-15 minutes. Let cool about 10 minutes before serving.