Melt butter in a large skillet over medium heat. Add onion; cook and stir until softened and browned, about 5 minutes. Add shrimp; cook and stir until opaque, 1 to 2 minutes. Stir in 2 tablespoons flour and white wine. Pour in milk gradually, stirring constantly with a wooden spoon; cook until white sauce thickens, 3 to 5 minutes.
Remove white sauce from heat. Stir in rice until evenly mixed. Add Parmesan cheese, dill, salt, and black pepper. Cool until mixture is easily handled, about 15 minutes.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Place 3 tablespoons flour in a shallow bowl. Whisk egg in a small bowl. Spread bread crumbs on a plate.
Form rice mixture into 8 equal balls. Roll 1 ball in flour, dip in beaten egg, and coat with bread crumbs. Repeat with remaining balls.
Deep-fry in hot oil until golden brown, about 3 minutes.
If there doesn't seem to be enough white sauce to evenly coat the rice in step 2, you can gradually stir in a little bit more milk until it seems to be enough.
We have determined the nutritional value of oil for frying based on a retention value of 10% after cooking. Amount will vary depending on cooking time and temperature, ingredient density, and specific type of oil used.
Parchment can be used for easier cleanup/removal from the pan.