Heat oil in a large pan over medium heat. Add chopped onions and sauté until they turn translucent and start to soften, about 5 minutes, filling the air with a sweet, fragrant aroma.
Add chopped tomatoes and cook until they break down and become saucy, about 8 minutes, stirring occasionally and letting the mixture simmer until thickened.
Stir in chopped green bell pepper along with pav bhaji masala, turmeric, and chili powder. Cook for another 2-3 minutes until fragrant and spices are well incorporated.
Add the mixed vegetables to the pan. If using leftover cooked veggies, toss them in now. Stir everything together, then reduce heat and simmer for 10-15 minutes, mashing occasionally with the back of your spoon to achieve a chunky, yet smooth mash.
While the bhaji simmers, slice the pav buns and toast them in a separate skillet with a little butter until golden and slightly crispy, about 2-3 minutes per side.
Finish the bhaji by stirring in lemon juice, adjusting seasoning if needed. The mixture should be thick, flavorful, and slightly chunky.
Scoop generous portions of the hot bhaji onto serving plates, and serve with toasted pav buns on the side for scooping and enjoying each bite.