In a large bowl, combine the warm milk, yeast, and 1/4 cup granulated sugar. Stir gently and let it sit for 5 10 minutes until the yeast is foamy. This shows the yeast is active.

Add the egg, melted butter, and vanilla extract to the yeast mixture. Whisk well to combine.

Gradually add the flour and salt to the wet ingredients, mixing with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms.

Turn the dough out onto a lightly floured surface and knead for 5 7 minutes until it's smooth and elastic. The dough should be soft but not sticky. Avoid adding too much extra flour.

Lightly grease a clean bowl, place the dough in it, and turn it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 1.5 hours, or until it has doubled in size. This first rise is important for flavor and initial aeration.

Once risen, gently punch down the dough to release the air. Turn it out onto a lightly floured surface. Roll the dough to about 1/2 inch thickness.

Using a doughnut cutter or two different sized round cookie cutters (one larger for the doughnut, one smaller for the hole), cut out your doughnuts. Gather the scraps, gently knead them together, and re roll to cut out more doughnuts.

This next step is the absolute secret to achieving fluffy, airy doughnuts. Place the cut doughnuts onto parchment lined baking sheets, leaving space between each. Cover them loosely with plastic wrap or a clean towel. Let them rise again in a warm spot for about 30 45 minutes, or until they look noticeably puffy and almost doubled in size again. When you gently poke one with a floured finger, it should spring back slowly, leaving a slight indentation. If it springs back immediately, it needs more time. If it collapses, it's over proofed. This second, shorter proofing period is crucial for developing the light, open crumb structure inside.

While the doughnuts are proofing, heat at least 3 inches of vegetable oil in a large heavy bottomed pot or Dutch oven over medium high heat until it reaches 350°F (175°C). Use a candy or deep fry thermometer to monitor the temperature closely. Maintaining the correct oil temperature is vital to prevent greasy doughnuts and ensure they cook evenly through to become fluffy.

In a shallow bowl, combine the 1/2 cup granulated sugar and cinnamon for coating.

Carefully lower 2 3 doughnuts into the hot oil, ensuring not to overcrowd the pot. Fry for 1 2 minutes per side, or until golden brown. Adjust the heat as needed to keep the oil consistently between 350°F and 365°F. Too low, and they absorb too much oil becoming heavy; too high, and they burn outside before cooking inside, resulting in a dense center.

Using a slotted spoon or spider, transfer the fried doughnuts to a wire rack set over paper towels to drain excess oil for just a minute.

While still warm, immediately toss the doughnuts in the cinnamon sugar mixture until evenly coated. The warmth helps the sugar adhere perfectly.

Repeat with the remaining doughnuts, always checking and adjusting the oil temperature before adding a new batch. Serve warm and enjoy that incredible, fluffy interior!