In a small bowl, combine 1 teaspoon of active dry yeast, 1 teaspoon of sugar, and 1/4 cup of warm water. Stir gently and let it sit for about 5-10 minutes until it becomes frothy.
In a large mixing bowl, whisk together 2 1/2 cups of all-purpose flour, 1/2 teaspoon of salt, and 1/4 cup of sugar.
In another bowl, mix the melted butter, egg, and skim milk. Once the yeast mixture is ready, add it to the wet ingredients and stir until combined.
Pour the wet mixture into the dry ingredients. Mix until a soft dough forms. If the dough is too sticky, add a little more flour, one tablespoon at a time.
Transfer the dough to a floured surface and knead gently for about 5 minutes until smooth and elastic.
Place the dough in a greased bowl, cover it with a clean cloth or plastic wrap, and let it rise in a warm place for about 1 hour or until doubled in size.
Preheat your oven to 350°F (175°C) while the dough is rising.
Once the dough has risen, punch it down gently to release the air. Roll it out on a floured surface to about 1/2 inch thick. Use a donut cutter or two round cookie cutters to cut out donut shapes.
Place the shaped donuts in a greased donut pan. Bake in the preheated oven for about 12-15 minutes or until golden brown.
Remove the donuts from the oven and brush them with melted butter while they are still warm to add extra flavor.
Once the donuts have cooled slightly, fill a pastry bag or zip-top bag with your choice of jelly. Poke a hole in the side of each donut and squeeze in the jelly until you feel a slight resistance.
Finish off your Baked Jelly Filled Donuts by dusting them lightly with powdered sugar. Serve immediately for the best experience!