Place potatoes, cauliflower, carrots, and peas in a deep pot with just enough salted water to cover them. Boil until completely fork-tender (about 15 minutes).
Drain the cooked vegetables, reserving the warm cooking water. Mash them thoroughly using a potato masher while they are hot until smooth.
Melt 2 tablespoons of butter in a deep pan. Add red onions and sauté until soft, translucent, and light gold around the edges.
Stir in the ginger-garlic paste and finely diced green bell pepper. Cook for 2 minutes until fragrant and the raw garlic aroma disappears.
Add chopped tomatoes. Cook down for 5-6 minutes until completely soft, mushy, and the butter begins to separate at the edges.
Add the Pav Bhaji Masala, Kashmiri chili powder, and salt. Stir well for 30 seconds to release their fragrant essential oils.
Fold in the mashed vegetables and 1 cup of the reserved cooking water. Mix well, cover, and simmer on low heat for 10-12 minutes.
Mash the mixture once more directly in the pan. Stir in another tablespoon of butter, lemon juice, and coriander. Adjust thickness with hot water if needed.
Slice pav buns in half. Melt butter on a hot skillet with a pinch of pav bhaji masala and coriander, then toast the buns open-faced until golden and crispy.