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  Prepare the Dough:
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  In a small bowl, mix the warm milk, warm water, and yeast. Let it rest for 5 to 10 minutes until it becomes foamy.
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  In a large mixing bowl, whisk together the flour, sugar, salt, and cinnamon.
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  Stir in the softened butter, eggs, vanilla extract, and the yeast mixture. Mix until the dough begins to come together.
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  Turn the dough out onto a lightly floured surface and knead for about 8 minutes until smooth and elastic. Alternatively, use a stand mixer fitted with a dough hook and knead on medium speed for 5 to 6 minutes.
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  Place the dough in a greased bowl, cover it with a clean towel, and let it rise in a warm spot for 1 to 1½ hours, or until it has doubled in size.

Shape and Fry the Donuts:

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  Once risen, roll the dough on a floured surface to about ½-inch thickness.
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  Use a donut cutter, or substitute with a large glass for the outer ring and a smaller cutter for the center hole. Arrange the cut donuts on a baking sheet lined with parchment paper.
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  Cover the donuts and let them rest for 30 to 40 minutes until they puff up.
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  Heat vegetable oil in a heavy pot to 350°F (177°C).
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  Carefully lower 2 to 3 donuts into the hot oil. Fry each side for 1 to 2 minutes or until golden brown. Remove with a slotted spoon and drain on a wire rack lined with paper towel.

Prepare the Maple Glaze:

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  In a medium bowl, whisk together powdered sugar, maple syrup, milk or cream, vanilla extract, and a pinch of salt until smooth.
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  Adjust the consistency by adding more milk if it’s too thick, or more powdered sugar if it’s too thin.

Glaze & Finish:

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  While the donuts are still slightly warm, dip the tops into the maple glaze.
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  Set them on a wire rack and sprinkle with toasted pecans and a pinch of flaky sea salt, if using.