Heat 1 tablespoon of butter in a pan. When it starts to foam, add the hing (asafoetida), half of the onions, the bell peppers, and mix well. Then add the ginger-garlic paste, half of the pav bhaji masala, half of the cilantro, and the kasoori methi. Cook until the onions and bell peppers soften. Add water if anything starts to stick or looks too dry in the pan.
When you are able to mash the bell peppers with the bottom of a metal cup, add tomatoes, beets, turmeric, chili powder, salt, peas, and the boiled potato, broken up into small pieces.
Mash everything together with the bottom of a metal cup or a potato masher to roughly mash the mixture together.
Push aside the mash to make room on the pan (or use a separate pan). Add 3 tablespoons of butter the open area. Top the butter with remaining pav bhaji masala. Mix the spices into the butter and let the spices bloom for 10-15 seconds.
Mix the spiced butter into the vegetable mash. Add a half cup of water and let the mixture cook until the butter separates and rises to the top, about 5-8 minutes.
Mash to desired consistency, or transfer half of the bhaji to a blender and blend until smooth, then recombine with the roughly mashed bhaji. Add water to adjust consistency if needed. Remove from heat and set aside.