Heat oil in a wide non-stick pan or dutch oven over medium heat, add carrots, celery, onion and thyme.

Saute the veggies until tender.

Add all-purpose flour to the tender veggies and combine well.

Add tomato paste and stir well.

Now, add ground beef, saute for a few minutes.

Add ¾ cup water and let come to a boil.

Lower the heat and cook the beef covered till it has cooked well and the water has dried off.

Remove from the heat, keep aside the beef filling.

Place peeled, diced potatoes in a wide sauce pan, cover the potatoes with water and let come to a boil.

Season the water with salt and lower the heat.

Cook the potatoes until a fork goes easily into the potatoes.

Drain the water from the cooked potatoes.

Add milk and 1 cup cheddar cheese to the potatoes and mash the potatoes until smooth without any lumps using a wooden spoon or potato masher.

Season the mashed potatoes with ground pepper and salt.

Preheat oven to 450 F.

In a baking pan, pour the beef filling as the lower layer into the pan and spread it evenly.

Drop the mashed potatoes over the filling and spread it evenly using a spatula.

Sprinkle the remaining ½ cup cheddar cheese over the mashed potatoes.

Bake for 15 to 20 minutes until the topping has browned and the filling is bubbling rapidly.

Let cool down for 5 minutes and using a spatula serve both the beef filling and mashed potatoes on each plate.