Make the glaze: mix together all the ingredients in a nonreactive (i.e., glass or plastic) bowl. Cover and refrigerate at least 30 minutes and up to 1 day.
Preheat the oven to 350 degrees. Put apples (they must be finely diced, almost minced) in a small bowl. Add lemon juice and hot water so that the apples are fully covered and let set while you're making the batter.
In a large mixing bowl, whisk together the flour, brown sugar, cinnamon, ginger, cloves, allspice, salt and baking powder (i.e., all the dry ingredients). Using your fingers, work in the cold butter like you would for pie crust or pastry dough until the mixture is fully incorporated.
In a medium bowl, whisk together the milk, egg, yogurt and molasses until well-blended. Slowly and carefully fold in the milk mixture in with the flour mixture; be careful not to overmix.
Spoon batter into a gallon-sized Ziploc bag and cut off a tiny 1/4" corner to use it like a pastry bag.
Drain the apples. Grease your mini-donut pan with the melted butter, then sprinkle a few apples (no more than a 1/2 teaspoon) into each donut cavity. Pipe the donut batter over the apples into the donut cavities so that the donut cavities are filled about 2/3rds of the way full. Be careful not to overfill, or you'll end up with puffy muffin-donuts (not that there's anything wrong with that, but it's just not a donut).
Bake in the oven for approximately 7 minutes, then remove the donuts from the oven. Let cool slightly, then invert the pan on a wire rack to let the donuts cool completely. Serve with yogurt glaze.