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 2 teaspoons salt. Let cool to room temperature. Heat about 2 inches vegetable oil in a heavy-bottomed pot over medium-high heat until a deep-fry thermometer registers 375 degrees F.
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 until golden, turning as needed, 1 to 2 minutes. Transfer to a paper towel-lined plate using a slotted spoon. Serve with chutney. Photograph by Andrew Mccaul