Start by boiling the potatoes and carrots until they're tender. You can do this in a large pot of boiling water for about 15-20 minutes. Once they are cooked, drain the water and let them cool.
Once the potatoes and carrots are cool enough to handle, grate or mash them in a large mixing bowl. You can use a potato masher or a fork to do this.
Add the chopped onion, fresh coriander, salt, black pepper to the potato-carrot mixture. Mix everything well.
In a separate bowl, beat the egg.Add the beaten egg to the potato and carrot mixture. This will help bind the patties together.
Mix in the bread crumbs until the mixture comes together and can be easily formed into patties. You can adjust the amount of bread crumbs if needed to achieve the right consistency.
Heat vegetable oil in a frying pan over medium heat.Shape the mixture into patties. You can make them as big or as small as you like.
Place the patties in the hot oil and cook for about 3-4 minutes on each side or until they are golden brown and crispy.
Once they are cooked through and have a nice golden crust, remove them from the pan and place them on a plate lined with paper towels to remove any excess oil.Serve the Potato and Carrot Patties hot