In a large mixing bowl, add All-Purpose Flour (3 1/3 cup), Granulated Sugar (1/4 cup) and Salt (1 teaspoon). Warm the Whole Milk (1 cup) to around 115 degrees C and melt the Butter (1/4 cup).
Add the Instant Dry Yeast (2 1/4 teaspoon) and the Granulated Sugar (1 teaspoon) to the milk, mix a bit, and let sit for five minutes.
In another bowl, whisk together the Egg (1) and the Butter. Add the yeast-milk and beat together.
Add the dry ingredients to the wet mix. Using a stand mixer, mix on low until the flour is incorperated, then increase to medium and beat until the dough is smooth.
Take the ball of dough and grease it. Form it into a disk and cover with plastic wrap. Let the dough rise for 3-4 hours in a microwave or a turned-off oven.
Flour a surface and roll out the dough. Using a cookie cutter or another round object, cut out the doughnut rounds and place on a baking sheet. Cover and let rise for 30 minutes.
Heat the oil and fry each round for 1-2 minutes per side, or until they're golden brown. Drain on a paper towel.
With a knife or a popsicle stick, make a hole to the middle of the doughnut. Pipe in the Strawberry Jelly (1/2 cup). Roll the doughnuts in Granulated Sugar (1/2 cup).