Preheat the oven to 400 degrees F. Line baking sheets with parchment paper and set aside.
For the dough: In a food processor, combine the flour, baking powder, sugar, and salt. Add the cold butter and pulse until the butter resembles pea-size pieces. Don't overmix. Drizzle in the cold water. The dough should form a solid mass. Add 1 or 2 additional tablespoons of water if needed for the dough to stick together. Remove the dough from the processor and refrigerate for at least 20 minutes.
Place the dough on a lightly floured surface. Flour a rolling pin and roll the dough out to 1/4 inch thick. Cut out circles of the dough using a 3-inch cookie cutter. Place the circles onto the paper-lined baking sheets and set in the refrigerator until ready to use.
For the filling: In a bowl, whisk together the eggs with 1/4 cup of the milk and set aside.
In a nonstick saute pan, melt 2 tablespoons of the butter on medium-low heat. Add the shallots and cook for 2 minutes, stirring occasionally, then add the kale and cook until wilted. Season to taste with salt and pepper. Add the egg and milk mixture and stir to create scrambled eggs. Remove and set aside in a bowl to cool slightly.
Using the same pan, add the remaining 2 tablespoons butter over medium heat. Stir in the flour to make a roux, stirring constantly for 4 minutes. Whisk in the remaining 1/4 cup milk slowly to avoid any lumps. Keep stirring and simmer for 5 minutes, until the mixture thickens slightly. Remove from heat and stir in the fontina. Season with salt and pepper.
Pour the cheese mixture into the kale and egg mixture, stir, and let cool slightly. It should look like creamy scrambled eggs.
Top each dough round with 1 to 2 teaspoons of filling, then fold in half to enclose to make the mini pies into half-moons. Seal the edges with a fork. Brush the top of each pie generously with the beaten egg.
Bake the pies for 15 to 20 minutes, or until the tops are flaky and golden. Cool slightly before serving.