Activate yeast by mixing warm milk and a pinch of sugar, then stir in the yeast and let it sit for 5-10 minutes until foamy.

In a stand mixer bowl, whisk together the flour, sugar, pumpkin spice, and salt.

Create a well in the dry ingredients, then add pumpkin puree, foamy yeast mixture, and eggs, mixing on low speed with a dough hook until a shaggy dough forms.

Increase mixer speed to medium-low and knead for 5 minutes; gradually add melted butter tablespoon by tablespoon, then continue kneading for another 10-15 minutes until the dough is smooth and elastic.

Lightly grease a large bowl, place the dough in it turning once to coat, then cover and let rise in a warm place for 1.5-2 hours until doubled in bulk.

Gently punch down the risen dough, cover tightly with plastic wrap, and refrigerate for at least 4 hours or preferably overnight to make it easier to handle.

On a lightly floured surface, roll out the chilled dough to approximately ½ inch thick.

Use a 3-inch donut cutter to shape donuts and a 1-inch cutter for center holes, gently re-rolling scraps once to cut additional donuts.

Carefully transfer the cut donuts and donut holes to parchment-lined baking sheets, ensuring sufficient space between each piece.

Loosely cover the donuts with plastic wrap or a clean towel and let them rise in a warm place for 45-60 minutes until visibly puffy and light.

Pour 2-3 inches of vegetable oil into a deep pot or Dutch oven and heat over medium heat to 350-375°F (175-190°C), using a candy thermometer to monitor.

Carefully lower 2-3 donuts into the hot oil using a slotted spoon, frying for 1-2 minutes per side until golden brown, noting that donut holes will fry faster for 30-60 seconds per side.

Remove fried donuts with the slotted spoon and place them on a wire rack set over a baking sheet to drain excess oil.

In a medium bowl, whisk together powdered sugar, maple syrup, 3 tablespoons of milk or cream, vanilla extract, and a pinch of salt until smooth.

Adjust the glaze consistency by adding more milk/cream teaspoon by teaspoon if too thick, or more powdered sugar tablespoon by tablespoon if too thin.

Once the donuts are cool enough to handle but still slightly warm, dip one side into the maple glaze.

Return the glazed donuts to the wire rack, glazed side up, allowing any excess glaze to drip off and set.

For an optional garnish, sprinkle with extra pumpkin pie spice or chopped pecans while the glaze is still wet.