Place cauliflower, bell pepper, carrots, cabbage, peas, potato, 6 cups water, 1 tablespoon pav bhaji masala, and 1 tablespoon salt in a large saucepan. Bring to a boil over high. Reduce heat to medium; simmer, stirring occasionally, until vegetables are very tender, about 15 minutes. Drain; set aside.
Melt ¾ cup plus 2 tablespoons butter in a large, deep skillet over medium-high until butter is bubbling. Add onion, garlic, and ginger; cook, stirring occasionally, until onion is translucent, 5 to 7 minutes. Stir in tomatoes, serrano chile, and remaining ½ cup water; cook, stirring occasionally, 3 minutes. Stir in tomato paste, red chile powder, and remaining 1 tablespoon pav bhaji masala; cook, stirring constantly, until mixture is the consistency of chunky tomato sauce, about 1 minute. Remove from heat. Add drained cauliflower mixture; mash using a potato masher until mixture resembles the consistency of chili, adding water as needed to loosen.
Stir lemon juice, cilantro, and remaining ¾ teaspoon salt into vegetable mixture in skillet. Cook over medium, stirring often, until mixture is warmed through, about 4 minutes. Season to taste with salt. Divide among 6 bowls; top each with 1 tablespoon butter. Garnish with additional red onion and cilantro, and serve with dinner rolls.
