Make the filling: Heat the butter in a small saucepan over medium heat. Add the flour and cook until smooth and bubbly, about 3 minutes. Add the milk slowly while whisking constantly. Bring to a simmer, stirring constantly, paying special attention to the corners of the saucepan. Add the paprika and salt and pepper, to taste. Stir in the corn and parsley, return to a simmer. Scrape the filling into a bowl and cool completely before filling wrappers.
To Form: Moisten the edges of 1 of the empanada wrappers with a fingertip dipped in warm water. Center a generous 1/3-cup of the filling on the wrapper. Bring the sides of the wrapper together to meet over the filling and pinch the sides together to seal and form a half-moon shape. Lay the half-moon flat on the work surface. Work you way around the edges, bringing about 1/2-inch of the bottom layer of dough up and over the top layer, to make a mini-pleat. Press as you go to seal the pleats. If you don't want to mess with crimping, just seal the edges all the way around with the tips of the tines of a fork.
Fry the Empanadas: (empanadas may also be baked; see Note below): Pour enough vegetable or canola oil into a large heavy skillet to fill about 3/4-inch up the sides. Heat over medium heat until the tip of the handle of a wooden spoon immersed in the oil gives off a lively sizzle, about 375 degrees F. Carefully slip as many of the empanadas into the oil as will fit without crowding. Cook until the dough is lightly browned, about 3 minutes. Carefully flip and repeat. Drain briefly on paper towels before serving. Repeat with remaining empanadas.
Note: To bake empanadas, preheat the oven to 375 degrees F. Line a baking sheet with parchment paper, or use a nonstick baking sheet. Bake until the empanadas are light golden brown, about 25 minutes. Cool a few minutes before serving.