01 - Combine milk, water, butter, and salt in a medium saucepan. Bring to a rolling boil over high heat. Reduce heat to low and dump in all flour at once. Stir vigorously with a wooden spoon until dough forms a ball and pulls away from pan sides, about 1-2 minutes. Transfer to a clean surface, let cool 3-4 minutes, then knead briefly until smooth. Cover with plastic wrap to prevent drying.
02 - Bring a pot of salted water to simmer. Add shrimp and cook 2-3 minutes until just pink and opaque. Drain immediately and transfer to ice bath to stop cooking. Finely chop shrimp into small pieces, about ¼-inch dice. Set aside.
03 - Melt butter in skillet over medium heat. Sauté onion 4-5 minutes until translucent and softened. Add garlic and cook 1 minute until fragrant. Sprinkle flour over mixture and stir constantly for 1-2 minutes to cook out raw taste. Slowly whisk in milk, stirring until thickened, about 2 minutes. Fold in chopped shrimp, lemon juice, parsley, salt, and pepper. Cook 2-3 minutes to meld flavors. Transfer to bowl, cover surface directly with plastic, and refrigerate until cooled completely, about 30 minutes.
04 - Roll dough on lightly floured surface to ⅛-inch thickness. Using a 3-inch round cutter, cut circles. Gather and reroll scraps once. Place 1 level teaspoon of cooled filling in center of each circle. Fold dough over to create half-moon shape. Press edges firmly with fingertips, then seal with fork tines. Transfer to parchment-lined baking sheet.
05 - Set up breading station: beaten eggs in shallow dish, breadcrumbs in another. Dip each rissoi in egg, allowing excess to drip off, then press firmly into breadcrumbs to coat all sides. Return to baking sheet.
06 - Pour 3 inches vegetable oil into heavy-bottomed pot or Dutch oven. Heat to 350°F on deep-fry thermometer. Fry rissois in batches of 4-5, 2-3 minutes per side, until deep golden brown. Transfer to wire rack or paper towels to drain.
07 - Arrange on serving platter. Serve warm or at room temperature with lemon wedges and remoulade or marinara sauce for dipping.