Place the potatoes in a microwave-safe plate. Microwave on high power for 5 minutes. If your potatoes are small, they may be fork tender already. If not, use a tong to turn the potatoes over and continue to cook in 2-minute increments until fork tender. To test doneness: Cut in half to see if the potatoes have cooked fully on the inside. The knife should slide through without resistance. If not, microwave in 1 minute bursts just until fully cooked.
Once the potatoes are cool enough to handle, peel and transfer to a medium bowl. Use a potato masher to mash them until no large lumps remain.
Place the remaining Aloo Tikki ingredients in a food processor (Note 1). Use the pulse function to chop so that the onions are finely chopped but not blended (~20 pulses). You don't want the onions to break down too much and end up releasing water. If you do notice any excess water in the mixture, tilt the food processor to drain it or dab it with a paper towel.
Add the chopped onion mixture to the mashed potatoes and mix to combine. Taste and adjust seasoning, adding salt to taste, red chili flakes/powder for more heat, and chaat masala/amchur/lemon juice for more tang. Keep in mind the flavors will mellow out once you fry them. Ideally, allow this mixture to rest, covered, in the refrigerator for 20 minutes (though I often skip this step).
Using your hands, shape ¼ cup of the mixture into a round, ½" thick patty about 2 ½-3 inches in diameter. If you find that the Tikkis are too soft or not holding their shape, mix in 1-2 tbsp breadcrumbs. Continue with the rest of the mixture. You'll have around 12 patties.
Place the egg and breadcrumbs (if using) in shallow bowls so that you can dip them as you cook.
Heat a large nonstick skillet, frying pan, or cast iron pan over medium heat. Add oil to lightly coat the bottom of the pan.
Dip both sides of each patty into the egg wash, and then the breadcrumbs (if using). Place 4-5 patties in the pan and cook for 3-4 minutes on each side, using a spatula to turn them over while using another spatula to hold them in place. Reduce heat if the patties are cooking too fast. Tip: To cook the edges/outer rim of the Tikkis evenly, move them to the corners of the pan where there's more oil.
Transfer the patties onto a paper towel lined plate. Repeat until you have finished pan-frying all the patties. Cook any leftover egg in the remaining oil and serve with the patties. Serve with green chutney or tamarind chutney (quick recipes in post), mint raita, or your favorite sauce.
