Activate yeast mixture:

In a large bowl or stand mixer bowl, combine warm milk, yeast, and 3 tablespoons sugar with a whisk. Allow to sit for 5 minutes; a foamy layer should appear. If not, discard and use fresh yeast.

Mix dough ingredients:

Incorporate flour, eggs, and salt. Using the dough hook on low speed, mix for 1 minute until combined. Scrape the bowl, then mix on medium speed for 2 minutes until the dough separates from the sides.

Knead in butter:

Scrape the bowl again. With the mixer on medium, add butter one tablespoon at a time. The dough will be very sticky and wet. Continue mixing for 5 minutes until it becomes smooth, elastic, and nearly dry to the touch. If still sticky, mix longer. For hand mixers, finish by hand on a lightly floured surface.

First rise:

Lightly oil a large bowl, place the dough inside, cover with oiled plastic wrap, and let rise in a warm spot until doubled in size, roughly 60 to 90 minutes.

Cook raspberry filling:

Meanwhile, prepare the raspberry filling: In a small saucepan, stir together frozen raspberries, 4 tablespoons sugar, and lemon juice. Heat until sugar dissolves, then simmer for 8 minutes until jam-like. Set aside to cool.

Make cheesecake filling:

Make the cheesecake filling: In a mixing bowl, whisk cream cheese, heavy cream, 2 tablespoons sugar, and vanilla until very thick. Refrigerate until needed.

Shape dough balls:

Line 3 large baking sheets with parchment and lightly grease. Dust a work surface with flour. Punch down the dough, transfer it to the floured surface, shape into a ball, and divide into 16 equal pieces (cut the ball into quarters, then each quarter into quarters). Roll each piece into a tight ball.

Second rise:

Arrange donuts on the prepared sheets with space between them. Loosely cover with oiled plastic wrap and let rise until nearly doubled, about 30 minutes.

Prepare fillings and coating:

Pour 2 cups sugar into a large bowl for coating. Transfer the raspberry compote and cheesecake filling to separate piping bags; snip the ends.

Heat oil:

Pour oil into a large heavy-duty Dutch oven or deep pot to a depth of about 2 inches. Heat to 330°F (165°C) to 350°F (165°C to 177°C). Use a thermometer; if unavailable, test with a small piece of dough—it should float and sizzle.

Fry donuts:

Carefully pick up donuts without deflating and gently place into hot oil, 3 to 4 at a time. Fry for 2 minutes per side until golden brown. Use a spider to transfer to a wire rack, then immediately toss in sugar and return to rack. Repeat with remaining donuts, monitoring oil temperature.

Fill donuts:

To fill: Use scissors or a sharp knife to make a hole in the side of each donut. Pipe raspberry filling into each, then cheesecake filling (use more cheesecake than compote). Donuts will feel plump and heavy when full. Enjoy warm.