In a small bowl, whisk together the warm water (110℉), ½ teaspoon of sugar, and the active dry yeast. Let it sit for 10 minutes until frothy and activated.

In a separate bowl, whisk together the warm milk (110℉), melted butter, sugar, egg, vanilla, and salt until combined. Whisk in the activated yeast mixture.

Add about 2 ½ cups of flour and mix until a loose dough begins to form. Turn the dough out onto a lightly floured countertop and knead, adding a little bit of flour at a time just until the dough is still tacky but no longer sticking to your hands when you knead it. Knead for 3-5 minutes or until the dough is soft, smooth, and a finger imprinted into the dough bounces back. Place in a bowl, cover, and let rise in a warm place for 1 hour or until the dough is doubled in size.

While the dough is rising, cook the peeled and chopped apples in 1 tablespoon of butter for a few minutes over medium heat until slightly tender. Let cool before assembling the fritters.

Punch down the risen dough and transfer to a lightly floured countertop. Stretch out with your hands or roll out using a rolling pin into a large rectangle about 12"x 20". Top half of the dough with the cooked apples, then sprinkle the cinnamon and allspice over the apples. Lastly, sprinkle about 1 tablespoon of flour over everything.

Fold the empty half of the dough over the filling, and then cut the layered dough into pieces around 1"x 1". Take a few pieces of the layered dough and form them into fritters. Press and fold them together, nestling the apples inside as best as you can. Add flour to help them stick together if the apples are juicy. They will not be perfect, but don't need to be!

Place the fritters on a parchment paper-lined baking sheet that has been sprinkled with a little bit of flour. Let rest and rise for 15-30 minutes while you make the glaze and heat the oil to 350℉ (at least 4 inches deep in a high-temperature safe Dutch oven or heavy pot).

Make the glaze by bringing the milk, butter, white sugar, and salt to a rolling boil for 2 minutes while whisking. Remove from the heat and whisk in the powdered sugar and vanilla until smooth.

Fry the risen fritters in the heated oil, maintaining a 350℉ temperature as best as you can. Fry on each side until dark brown in color. Remove from the oil and let sit on a paper towel-lined plate for a few minutes to soak up excess oil before transferring to a wire rack.

Coat the slightly cooled fritters in the warm glaze, being careful not to burn your fingers (use a utensil), and place them back on the wire rack for excess glaze to drip off. Enjoy!