In a small saucepan, heat milk to a boil. Remove from heat, add sugar and cool to 110 degrees F. Mix together warm milk and yeast and let sit for a few minutes. Transfer to a large bowl. Sift together flour, salt, cinnamon and nutmeg. Using a wooden spoon, add flour mixture to the milk mixture. Mix in egg yolks, melted butter and lemon zest. Turn mixture out onto a well-floured surface. Knead to form a dough. Place dough in a clean, lightly oiled bowl and cover with a towel. Place in a warm, draft-free area and let rise for 1 1/2 hours. Remove dough from bowl and place on a floured surface. Roll out the dough to 1/8-inch thickness. Using a 3-inch round cookie cutter, cut the dough into 24 circles. Place 12 of the circles on a parchment lined sheet pan. Spoon 1 teaspoon of filling into the center of each circle. Brush beaten egg around the perimeter of each of the 12 circles. Place another circle on top of the raspberry filling and press around the edges to seal. Cover the tray with a towel and let rise another 30 minutes in a warm, draft-free location. In a large, deep pot, heat the oil to 325 degrees F. When the doughnuts have risen, fry them in the oil, a few at a time, turning often until both sides are golden brown, about 6 minutes. Remove to a paper towel-lined plate and sprinkle with powdered sugar.
In a saucepan, combine 1 pound raspberries, sugar and lemon juice. Cook over low heat until sugar dissolves and raspberries begin to break down. Remove from heat and transfer to a food processor. Puree until smooth. Strain through a fine mesh strainer into a saucepan. Cook over medium heat for 10 to 15 minutes, stirring occasionally. Add in 1/2-cup whole raspberries. Cook for 1 more minute. Remove from heat, whisk in cornstarch mixture. Return to high heat, bringing to a boil, whisking constantly until mixture is thick. Remove from the heat and cool.
Recipe courtesy Food Network Kitchens