Prick the potatoes all over with a fork and microwave until tender, 8 to 10 minutes. Peel the potatoes, then transfer to a large bowl and mash with a fork until almost smooth. Mix in the cottage cheese, peas, curry powder, 2 tablespoons flour, and salt. Let cool to room temperature.
Meanwhile, whisk the eggs in a shallow bowl. Put 1 cup flour in another bowl and the panko in a third bowl.
Form the potato mixture into about 24 golf ball-size portions, then gently flatten into 2-inch patties. Dredge each patty in the flour, shake off any excess, dip in the eggs, then dredge in the panko, turning to coat. Fry the patties in batches in a deep fryer until golden, turning as needed, 1 to 2 minutes. Transfer to a paper towel-lined plate using a slotted spoon. Serve with chutney.