Preheat the oven to 400°F.
Place the rice, 4 cups of water, cumin, garlic and a pinch of salt in a large saucepan. Bring to a simmer, reduce heat to low, cover, and cook for 20-30 minutes, until the grains are tender. Fold in the peas.
In a large skillet, heat the olive oil, ginger, garlic and vindaloo paste until fragrant. Add the fresh and canned tomatoes and bring to a simmer. Add the salt and pepper and cook for 10 minutes, until flavorful. Remove from the heat and stir in the cilantro.
Place the potatoes in a steamer basket inside a pot with 1 inch of water. Bring to a simmer, cover, and steam the potatoes until fork-tender, 12-15 minutes.
Combine the spice rub for the chicken and coat the chicken in the spices and oil. Place on a baking sheet and roast until cooked through, 8-10 minutes.
Combine all of the mint yogurt ingredients in a small bowl.
To serve, divide the rice between plates. Top with potatoes, chicken, vindaloo sauce, mint yogurt and naan.