In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, and yeast until well combined. Slowly add in the warm milk, melted butter, eggs, and vanilla extract. Mix these ingredients until a smooth, sticky dough forms, which may take about 3-5 minutes.

Transfer the dough onto a lightly floured surface and knead for approximately 10 minutes, or until it becomes elastic and smooth.

Place the kneaded dough into a greased bowl, covering it with a clean kitchen cloth. Allow it to rise in a warm spot for about 1 hour, or until it has doubled in size.

Once risen, punch down the dough to release any air. Roll it out on a floured surface to about ½-inch thickness. Use a round cutter to cut out circles, placing them on parchment paper.

Heat oil in a deep pot to 350°F (175°C). Carefully add the dough circles to the hot oil, frying them in batches for about 2-3 minutes per side, or until golden brown.

Once the Bomboloni have cooled to room temperature, use a piping bag fitted with a large round tip to inject them with pastry cream.

Finally, roll the filled Bomboloni in powdered sugar before serving.