Cook the potatoes, cauliflower, peas, and carrot in a large pot of salted water until completely tender, then drain and roughly mash them together. Heat the oil and 1 tablespoon of butter in a large skillet or tawa over medium heat and sauté the chopped onion until soft and lightly golden. Add the ginger, garlic, and green bell pepper and cook for 2–3 minutes until fragrant. Stir in the tomatoes, turmeric, chili powder, pav bhaji masala, and salt, then cook until the tomatoes become soft and the mixture turns into a thick masala. Add the mashed vegetables and water, then use a potato masher to mash everything together directly in the pan. Simmer for 10–15 minutes, stirring frequently, until the bhaji becomes thick, smooth, and richly flavored. Stir in the lemon juice and remaining butter just before serving. Slice the pav buns and toast them on a hot pan with a little butter until golden and crisp on the edges. Serve the hot bhaji with buttered pav, chopped onion, fresh coriander, and lemon wedges.