Peel, wash, and chop all the vegetables as mentioned. potato, cauliflower, and carrots will be boiled and then mashed so you can chop them roughly.
I puree tomatoes because that's how my kids like it. You can either puree them or chop them finely.
Heat butter in a thick bottomed pan. Add chopped onions, capsicum, and green chilies. when onions are almost done add ginger and garlic. saute till onions turn translucent. Now goes in red chili powder and Pav Bhaji masala. pour in tomato puree or chopped tomatoes and let it cook on medium flame.
Boil or pressure cook potato, carrots, and cauliflower in water. you can add some salt also. Mash the veggies.
when tomatoes start leaving oil, add the mashed veggies to them. Add the salt now.
Cook for another 5-7 minutes. Add more water to get the desired consistency. when it's almost done, add the boiled peas, and coriander leaves. Taste and check for salt and spices and add whatever is required. Add lemon juice just before serving the bhaji.