Prepare the Dough:
In a small bowl, dissolve the yeast in the lukewarm milk and let it sit for about 5 minutes, or until frothy.
In a large bowl, combine the sugar, eggs, butter, and vanilla extract. Mix in the yeast mixture.
Add the flour and salt, mixing until a soft and pliable dough forms.
Knead the dough on a floured surface for about 5-7 minutes, until it becomes smooth and elastic.
Place the dough in a greased bowl, cover with a clean cloth, and let it rise in a warm place for about 1 hour, or until doubled in size.
Prepare the Filling:
In a medium bowl, blend the cream cheese, sugar, and vanilla extract until smooth.
Mix in the finely chopped strawberries and set aside.
Shape and Fry the Doughnuts:
Punch down the risen dough and turn it out onto a floured surface.
Roll the dough to about 1/2 inch thickness.
Use a doughnut cutter or two round cutters (one larger and one smaller) to cut out doughnut shapes.
Heat oil in a deep fryer or large pot to 350°F (175°C).
Fry the doughnuts, a few at a time, for about 1-2 minutes per side, or until golden brown.
Transfer the fried doughnuts to a paper towel-lined plate to drain.
Stuff the Doughnuts:
Once the doughnuts have cooled slightly, use a piping bag with a small tip to fill each doughnut with the strawberry cheesecake filling.
Coat the Doughnuts:
In a small bowl, mix the granulated sugar and ground cinnamon.
Roll the filled doughnuts in the cinnamon sugar mixture until fully coated.