Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Chop the peppers and sweet potatoes into evenly sized chunks. Arrange on a baking sheet in a single layer. Drizzle with 4 tablespoons olive oil and season with 2 teaspoons garam masala and 1 teaspoon cumin. Toss and roast in the oven for 20 minutes.
Meanwhile, heat the remaining 2 tablespoons olive oil in a skillet. Add the garlic and chili pepper and cook over low heat until fragrant, for about 30 seconds. Add the remaining 2 teaspoons garam masala and 1 teaspoon cumin. Cook for a minute, stirring.
Add the canned tomatoes, water, and chopped cilantro. Season with salt and cook, over medium heat, for 20 minutes more.
Finally, add the roasted peppers and sweet potatoes and cook for 5-10 minutes more. If the curry isn’t thick enough to your liking, cook more. If it gets too thick, add more water.
Drizzle with lime juice before serving. Garnish with chopped cilantro. Serve with rice.