In a small bowl, stir the warm milk with sugar and yeast. Let sit 5–8 minutes until foamy. If it doesn’t foam, your yeast might be old—try again with fresh yeast.

In a large bowl (or your mixer), whisk eggs and melted butter. Add the foamy yeast mixture. Stir in 2 cups of flour and the salt until combined. Add remaining flour, 1/2 cup at a time, until the dough pulls away from the sides but is still slightly tacky.

Knead by hand on a floured surface for 6–8 minutes, or use a mixer with a dough hook for 4–5 minutes. Place dough in a lightly greased bowl, cover with a damp towel, and let rise in a warm spot until doubled—about 1 to 1.5 hours.

Beat the softened cream cheese with powdered sugar and vanilla until smooth. Stir in the strained raspberry puree until swirled but not fully mixed for a marbled effect, or combine fully for an even color. Add heavy cream 1 tbsp at a time until the filling pipes smoothly. Transfer to a piping bag and chill until you’re ready to fill.

Turn the risen dough onto a floured surface and roll to 1/2-inch thickness. Cut rounds with a 3-inch cutter. Place on a parchment-lined tray, cover lightly, and let rest 20–30 minutes until puffy.

Heat oil to 350°F (175°C). Fry donuts a few at a time, 60–90 seconds per side, until golden brown. Use a slotted spoon to transfer to a paper towel-lined rack to drain.

Preheat oven to 375°F (190°C). Brush the tops of rounds with melted butter and bake 10–12 minutes until golden. These won’t get the same deep-fried crust, but are delicious and quicker to clean up.

Once donuts are slightly cool but still warm, insert a piping tip into the side of each donut and pipe in about 2–3 tablespoons of the raspberry cheesecake filling. For neatness, twist the tip as you pull out.

Whisk glaze ingredients until smooth. Dip the filled donuts tops into the glaze or drizzle with a spoon. Finish with a fresh raspberry or a sprinkle of zest.

These are best the day they’re made, but the filling can be made ahead and stored in the fridge for up to 2 days. If you need to keep donuts, store them in an airtight container for up to 24 hours—refresh briefly in a warm oven if you like.