In a small bowl, combine warm milk, warm water, and yeast. Let it sit for 5–10 minutes until foamy.

In a large bowl, whisk together flour, sugar, salt, and cinnamon.

Add softened butter, eggs, vanilla extract, and the yeast mixture to the dry ingredients.

Mix until the dough starts to form.

Transfer the dough to a floured surface and knead for about 8 minutes until smooth and elastic, or use a stand mixer with a dough hook on medium speed for 5–6 minutes.

Place the dough in a lightly greased bowl, cover with a towel, and let rise in a warm place for 1 to 1 ½ hours or until doubled in size.

Once risen, roll out the dough on a lightly floured surface to about ½ inch thick.

Cut out donut shapes using a donut cutter or a large glass and a smaller cutter for the center. Place them on a parchment-lined baking sheet.

Cover and let rest for 30–40 minutes, until puffy.

Heat vegetable oil in a heavy-bottomed pot to 350°F (177°C).

Fry 2–3 donuts at a time for 1–2 minutes per side, until golden brown. Remove with a slotted spoon and drain on a wire rack lined with paper towels.

In a medium bowl, whisk together powdered sugar, maple syrup, milk (or cream), vanilla extract, and a pinch of salt until smooth. If the glaze is too thick, add a little more milk; if too thin, add more powdered sugar.

While the donuts are still slightly warm, dip the tops into the glaze.

Place on a wire rack and, if desired, sprinkle with toasted pecans and flaky sea salt.

Serve and enjoy your donuts with your favorite drink.