Preheat the oven to 425 degrees . In a large pot, cover the potatoes with 2 inches of water. Bring to a boil, salt the water and reduce the heat to medium. Cook until tender, about 12 minutes.
Meanwhile, in a large skillet, melt 1 tbsp. butter over medium-high heat. Add the carrots and onion and cook, stirring occasionally, until the vegetables start to soften, about 5 minutes; season with salt and pepper. Stir in the lentils, tomatoes, ginger and garam masala. Cook, stirring occasionally, until the sauce thickens, 3 to 5 minutes. Stir in the peas, season and transfer to four 2-cup ramekins.
Drain the potatoes; return to the pot. Add the yogurt and remaining 5 tbsp. butter. Mash until smooth; season. Divide the mashed potatoes among the ramekins, spreading them over the vegetables. Bake until golden in spots, 10 to 15 minutes. Sprinkle with the chives.