Prepare the Donut Dough:**
- In a small bowl, dissolve the yeast in the warm milk. Let it sit for about 5 minutes, or until it becomes foamy.
- In a large mixing bowl, combine the sugar, eggs, melted butter, and vanilla extract. Add the yeast mixture and mix until combined.
- Gradually add the flour and salt, mixing until a soft dough forms. Knead the dough on a lightly floured surface for about 5-7 minutes, or until smooth and elastic.
- Place the dough in a lightly greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.
**Prepare the Strawberry Cheesecake Filling:**
- In a medium bowl, beat the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy.
- Gently fold in the chopped strawberries until evenly distributed.
- Transfer the filling to a piping bag fitted with a medium round tip and refrigerate until ready to use.
**Shape and Fry the Donuts:**
- Once the dough has risen, punch it down to release the air. Roll the dough out on a floured surface to about ½-inch thickness.
- Use a round cookie cutter (about 3 inches in diameter) to cut out donut shapes. Re-roll the scraps as needed to use all the dough.
- Place the cut donuts on a parchment-lined baking sheet and cover them with a kitchen towel. Let them rise for another 30 minutes, or until puffy.
- Heat vegetable oil in a deep fryer or large heavy-bottomed pot to 350°F (175°C).
- Carefully fry the donuts, a few at a time, for about 1-2 minutes per side, or until golden brown. Use a slotted spoon to transfer the donuts to a paper towel-lined plate to drain any excess oil.
**Fill the Donuts:**
- While the donuts are still warm, roll them in granulated sugar until coated.
- Allow the donuts to cool slightly, then use a small knife to make a small incision in the side of each donut.
- Insert the tip of the piping bag into the incision and fill each donut with the strawberry cheesecake filling until it feels slightly heavy.
**Serve:**
- Optionally, garnish the tops of the filled donuts with a few pieces of diced strawberries for an extra touch of flavor and color.
- Serve the Strawberry Cheesecake Filled Donuts fresh, and enjoy the delicious combination of creamy cheesecake and sweet strawberries with every bite.