2 cups all-purpose flour, plus more for kneading and shaping
Vegetable oil, for bowl
For Assembly and Serving
2 large eggs
1 cup dried breadcrumbs
Vegetable oil, for deep frying
Chutneys or dipping sauces, if desired
Make the filling:
In a sauté pan, melt the butter over medium heat. Add the onion and garlic and sauté until the onions is translucent, about 5 minutes. Add the shrimp and sauté, stirring often, until they turn light pink, 3 to 4 minutes. Stir in the milk and season with salt and pepper to taste.
In a small bowl, stir together the flour and 1 tablespoon water to make a slurry. Add the slurry to the shrimp and cook, stirring occasionally, until the liquid is slightly thickened, 3 to 5 minutes. Remove from the heat and stir in cheddar and nutmeg. Refrigerate until chilled.
Make the pastry:
In a saucepan, combine the milk and butter and cook over medium-high heat, stirring occasionally with a wooden spoon to prevent the milk from scalding.
Once the butter is melted, reduce the heat to medium, add the flour, season with salt, and stirring constantly, cook until a smooth dough forms and it comes together in a ball and begins to pull away from the side of the pan, 5 to 8 minutes. Tend to the mixture carefully during this process to prevent it from burning; if it becomes too hot and begins to burn before coming together and clearing the sides of the pan, remove the pan from the heat for 30 seconds to cool the dough, then reduce the heat and set the pan back over the heat, stirring until a dough forms. Once a dough forms, remove it from the heat, turn it out into a bowl, and set aside until it’s cool enough to handle.
Once the dough has cooled enough to handle (but is still warm), dust a clean work surface with flour and knead the dough until it’s smooth and springs back when poked with your finger, 4 to 6 minutes.
Oil a medium bowl, add the dough, cover with a damp towel, and set aside for 30 minutes.
Assemble the rissóis:
On a lightly floured work surface, roll the dough out to ⅛ inch thick. Use a 2- inch round cookie or biscuit cutter to cut 2-inch rounds out of the dough, resulting in approximately 24 2-inch rounds.
Fill a small bowl with water and lightly dab water around the edges of a dough round. Spoon about 1 tablespoon filling in the center of the round and fold the dough over to form a half-moon shape. Press the edges together to close securely. Repeat with the remaining dough rounds and filling.
In a small bowl, lightly beat the eggs. Place the breadcrumbs in a second bowl. Dip both sides of the turnover in the egg with one hand and shake lightly to remove excess. Using your dry hand, dredge the pastry in the breadcrumbs, shaking to remove any excess. Transfer to a plate and repeat with the remaining turnovers.
Line a plate with paper towels. Pour 2 inches oil into a sauté pan and heat the oil over medium-high heat to 325 on an instant read thermometer. Working with 5 or 6 rissóis at a time (do not overcrowd the pan), use tongs to place the turnovers into the oil. Cook until the pastries are golden brown on the bottom, about 2 minutes, then flip over and cook until the filling is cooked through, an additional 2 to 3 minutes. Transfer to the paper towels to drain and season with salt.
Serve while still hot with a variety of chutneys or dipping sauces.