Step 1: Activate the yeast. In a small bowl, combine the warm milk with 1 teaspoon of granulated sugar and sprinkle the active dry yeast on top. Let it sit for 5-10 minutes until it becomes foamy and bubbly. This indicates your yeast is active.
Step 2: Prepare the donut dough. In a large mixing bowl (or the bowl of a stand mixer fitted with a dough hook), combine the remaining ¼ cup granulated sugar, salt, beaten eggs, melted butter, and the activated yeast mixture. Gradually add 4 cups of the all-purpose flour, mixing until a shaggy dough forms. If using a stand mixer, knead on low speed for 8-10 minutes until the dough is smooth, elastic, and pulls away from the sides of the bowl. If kneading by hand, knead on a lightly floured surface for 10-15 minutes. Add more flour (up to ½ cup) if the dough is too sticky, but aim for a slightly tacky consistency.
Step 3: First rise. Lightly grease a large clean bowl with a little vegetable oil. Place the dough in the bowl, turning it once to coat. Cover the bowl tightly with plastic wrap or a clean kitchen towel. Let the dough rise in a warm, draft-free place for 1 to 1.5 hours, or until it has doubled in size. This process is crucial for light, airy donuts.
Step 4: Prepare the raspberry filling. While the dough is rising, combine raspberries (fresh or frozen), ½ cup granulated sugar, lemon juice, and 2 tablespoons of water in a small saucepan. Bring to a simmer over medium heat, stirring occasionally. In a separate small bowl, whisk together the cornstarch with 1 tablespoon of cold water to create a slurry. Add the cornstarch slurry to the simmering raspberry mixture, stirring constantly until it thickens. Cook for another minute, then remove from heat. For a smoother filling, you can gently mash the raspberries or pass the mixture through a fine-mesh sieve. Let the filling cool completely before use; it will thicken further as it cools.
Step 5: Shape the donuts. Gently punch down the risen dough to release the air. Turn it out onto a lightly floured surface. Roll the dough to approximately ½-inch thickness. Using a 3-inch round cutter (or a clean glass rim), cut out donut shapes. You can gather and gently re-roll the scraps once to cut out more donuts. Place the cut donuts on parchment paper-lined baking sheets, leaving a couple of inches between each. Cover loosely with plastic wrap or a clean kitchen towel.
Step 6: Second rise. Let the shaped donuts rise again in a warm, draft-free place for 30-45 minutes, or until they are visibly puffy. This second rise contributes to their ultimate fluffy texture.
Step 7: Fry the donuts. Heat 2-3 inches of vegetable oil, canola oil, or shortening in a large heavy-bottomed pot or Dutch oven to 350-360°F (175-180°C). Use a candy thermometer to maintain the correct temperature. Carefully lower 2-3 donuts at a time into the hot oil, ensuring not to overcrowd the pot. Fry for 1-2 minutes per side, or until golden brown. Use a slotted spoon or spider to flip and remove the donuts. Place the fried donuts on a wire rack set over paper towels to drain excess oil. Allow them to cool slightly, but they should still be warm.
Step 8: Fill and finish. Once cooled enough to handle, transfer the raspberry filling into a piping bag fitted with a long, thin pastry tip (like a Bismark tip). Gently insert the tip into the side of each donut and pipe in about 1-2 tablespoons of filling until the donut feels plump. Roll the filled donuts immediately in granulated sugar or powdered sugar to coat completely. Serve warm and enjoy your homemade Raspberry Filled Donuts!