Set your oven to 420 F. Toss the potato, carrot, and cauliflower together in a bowl with 2 tbsp vegetable oil and 1 tbsp salt. Place the vegetables on a sheet pan, then roast until tender, about 15 minutes. Remove from the oven and set aside.
Put 2 tbsp vegetable oil into a Dutch oven or deep saute pan. Heat oil on medium high. Add the red onion, bell peppers, and green chili. Cook while stirring occasionally for 10 minutes until the onions are translucent. Add the garlic and ginger and cook while stirring for 2 minutes. Add the tomato paste, coriander, ground cumin, paprika, red chili powder, and 4 tbsp butter then stir for 2-3 minutes until the mixture slightly darkens.
Pour in 2 cups of water, then the frozen peas and cook while stirring for 5 minutes. Add in the roasted vegetables and the remaining butter. Add salt to taste.
Remove from the heat and stir in the garam masala, the fresh lime juice, and the chopped cilantro. Add more salt to taste.