Warm the milk and apple cider until just warm to the touch. Be careful not to make it too hot; around 110-115°F is perfect.
In a stand mixer, combine warm milk, 1 tablespoon of brown sugar, and yeast. Let it stand for 5-10 minutes until frothy.
In another bowl, whisk together flour, spices, and salt.
Add lemon zest, egg, softened butter, vanilla, and remaining brown sugar to the yeast mixture. Mix on low and gradually add dry ingredients.
Once all the flour is incorporated, mix on high for about 5 minutes until the dough is smooth and elastic.
Remove the dough, knead it, shape it into a ball, and let it rise in a warm place until doubled in size (about 30-45 minutes).
While the dough rises, prepare the apple mixture by caramelizing apples and adding cranberries. Cool in the fridge.
Roll the risen dough into a square, spread the cooled apple mixture on half, and fold the other half over. Seal the edges.
Cut the dough into strips, then at a 45º angle to create a crisscross pattern.
Shape the pieces into a log, cut into 8-10 pieces, and let them rise for an additional 20 minutes.
Heat canola oil to 350˚F in a pot. Fry the fritters until golden-brown (1-2 minutes per side). Drain on a rack.
Whisk together the glaze ingredients and coat the warm fritters. Let the glaze set for 10 minutes. Enjoy your homemade holiday fritters!