Step 1Combine the potatoes, carrot, cauliflower, bell pepper and peas in a large (3 1/2 --quart) saucepan. Add 2 3/4 cups water and one-half teaspoon salt. Bring to a boil. Cook on medium-high heat until very tender, about 30 minutes. Do not drain. Use a potato masher to mash the vegetables and the liquid together to make a fine paste. Set aside.
Step 2Heat the oil in a large nonstick skillet. Add the cumin seeds and fry until they sputter, about 1 minute. Add 2 1/2 cups diced onions and fry until translucent.
Step 3Add the pav bhaji masala, ginger-garlic paste, salt to taste and the chili powder. Stir to combine. Add the tomatoes; stir and cook 4 minutes. Add the mashed vegetable paste to the onion-tomato mixture and mix well. Cook 5 minutes.
Step 4Add the butter and lemon juice. Stir to combine.
Step 5Remove the vegetables from the pan, spooning into a serving bowl and leaving about a tablespoon of the mixture in the pan. Add the remaining 1 tablespoon butter to the pan and stir to incorporate as it melts. Place the rolls cut side down in the pan and cook in the butter-vegetable mixture until lightly toasted.
Step 6To serve, garnish the mashed vegetables with cilantro leaves. Serve with the toasted rolls, chopped onions, whole serrano chiles and lemon wedges.