Place the cubed potatoes, cauliflower florets, and green peas in a large saucepan. Cover with water, add a pinch of salt, and bring to a boil over medium-high heat. Cook for 12 to 15 minutes until all vegetables are fork-tender.

Drain the cooked vegetables, reserving the cooking water. Using a potato masher, mash the hot vegetables thoroughly until smooth and uniform. Set aside.

Heat 2 tablespoons of butter and 1 tablespoon of oil in a large skillet or kadai over medium heat. Add the finely chopped onions and sauté until translucent. Add the capsicum and ginger-garlic paste, cooking for 2 minutes until the raw aroma disappears. Stir in the chopped tomatoes, cooking until they soften and blend into a thick paste.

Add 1 tablespoon of pav bhaji masala, Kashmiri red chili powder, and salt to the tomato-onion mixture. Stir well and cook for 1 minute. Add the mashed vegetables and 1 1/2 cups of water, mixing thoroughly to combine.

Reduce the heat to medium-low and let the bhaji simmer for 10 to 12 minutes, stirring occasionally and mashing further with the back of a spoon. Adjust consistency with warm water if the mixture becomes too thick. Stir in the remaining 1 tablespoon of pav bhaji masala and half of the chopped coriander leaves just before turning off the heat.

Slice the pav horizontal-wise without cutting all the way through. Melt the remaining butter on a hot griddle or pan, place the bread on the butter, and toast until golden brown on both sides. Serve hot bhaji topped with a pat of butter and remaining coriander, alongside toasted pav and lemon wedges.