Melt 2 tablespoons of the butter in a large, high-sided skillet, and add the onion. Cook over medium heat until soft and sweet, about 10 minutes. Add the rice and salt and cook, stirring, until well coated in butter, about 2 minutes. Pour in the white wine and cook, stirring, until it evaporates. Add 1/2 cup water and cook, stirring frequently, until it has been absorbed. Repeat, adding 1/2 cup water at a time, until the rice swells and becomes tender. This should take about 15 minutes and about 3 to 3 1/2 cups water. The texture of the risotto should be softly flowing but not soupy.
Stir in the Parmesan, and transfer the risotto to a wide bowl. When it is cool enough to touch, fold in the cheese curds.
Line an 8-inch-square baking dish with plastic wrap, leaving plenty of overhang on all sides. Pour the risotto into the dish, smooth the top, and cover with the overhanging plastic. Refrigerate until firm, about 3 hours, or as long as overnight.
Before serving, clarify the remaining 8 tablespoons butter: Heat the butter in a small skillet over medium heat until it foams and starts to turn dark blond on top, 5 to 7 minutes. Remove from the heat and let the butter sit for a few minutes. Then tilt the skillet toward you and gently spoon off and discard the top layer of foam. Pour the clear golden butter into another bowl, discarding the dark dregs at the bottom of the skillet.
Unmold the risotto cake onto a cutting board. Cut it into eight 1-inch-wide slabs, and then cut each rectangle into thirds to make 24 pieces. Put the rice flour in a shallow dish. Dip the tops and bottoms of the risotto cakes in the flour, and transfer them to a platter or baking sheet.
Preheat the oven to 250 degrees F.
Heat a large nonstick saute pan or cast-iron skillet over medium-high heat. Add enough clarified butter to lightly coat the bottom, and when it's hot, add as many risotto cakes as will fit in the pan. Fry until a dark golden brown crust forms on both sides and the cheese inside is melted, about 4 minutes. Keep the fried risotto cakes warm in the oven while you fry the rest of them. Serve immediately.
Adapted from "The New Midwestern Table" by Amy Thielen (c) Clarkson Potter, 2013. Provided courtesy of Amy Thielen. All rights reserved.