Heat oil and butter in a pan; add onions, ginger+garlic paste, turmeric and cook till the onions turn translucent.
Next add the green peppers, tomatoes, green peas, chili powder and salt. Cover and cook till the veggies are very tender.
Stir in mashed potatoes and mix well. Mash with a potato masher until the veggies are smooth and well combined. Add a splash of water of water if the mixture looks too dry.
Add pav bhaji masala and simmer for 5~8 minutes. Taste and adjust the seasoning accordingly.
Toast the buns with butter. Spread with green chutney on both the buns. On the bottom bun put bhaji, onion, cheese, ketchup on the top bun. Toast until the cheese is melted, if desired. Serve right now.