Heat a tablespoon of oil in your large skillet over medium-high heat. Add chopped onions and cook until translucent and fragrant, about 3-4 minutes.
Add the ground meat to the skillet, breaking it apart with your spatula. Cook until browned and no longer pink, about 8-10 minutes. Drain excess fat if needed.
Stir in chopped carrots, peas, and minced garlic. Continue cooking until vegetables are tender and fragrant, about 5 minutes.
Pour in the broth and sprinkle with thyme, salt, and pepper. Simmer gently until the mixture thickens slightly, about 5 minutes, stirring occasionally.
While the filling simmers, warm the mashed potatoes if needed and whip or stir until smooth and fluffy. Add butter and milk for extra creaminess.
Preheat your oven to 200°C (390°F). Spread the meat filling evenly in your baking dish.
Spoon the mashed potatoes over the filling, spreading with a spatula to cover completely. Create some ridges on top for a crispy texture.
If desired, sprinkle shredded cheddar cheese over the mashed potatoes for extra flavor and a golden crust.
Bake in the preheated oven for 20-25 minutes, until the top is golden brown and bubbling around the edges.
Remove from the oven and let rest for about 5 minutes. Serve slices warm, enjoying the crispy topping and savory filling.