Prepare the pastry cream in advance and refrigerate it for several hours to allow proper chilling.

In a large mixing bowl or the bowl of a stand mixer, stir together 2 cups (250 g) of flour, yeast, sugar, and salt.

Warm the milk to 110–115°F (43–46°C) using the microwave. Add the warmed milk to the dry mixture and stir until fully incorporated.

Mix in the melted butter, beaten eggs, and vanilla extract until the dough begins to come together.

Gradually add the remaining flour while mixing with a wooden spoon, spatula, or dough hook until the dough is smooth, cohesive, and slightly tacky but not sticky. Adjust the flour quantity based on texture if needed.

Place the dough into a lightly oiled bowl, cover it tightly with plastic wrap, and let it rise in a warm, draft-free location until doubled in volume, approximately 30 to 60 minutes.

Turn the risen dough out onto a lightly floured work surface. Roll or pat to a thickness of ¾ inch (2 cm), cut into rounds using a 3-inch biscuit cutter, and place them on a parchment-lined baking sheet with at least 1 inch (2.5 cm) of space between each. Cover and let rise until puffed and nearly doubled, about 30 minutes. Meanwhile, begin heating the frying oil.

Pour vegetable oil into a medium-sized heavy-bottomed saucepan to a depth of 2–3 inches (5–8 cm) and attach a candy thermometer. Heat the oil over medium heat until it consistently holds a temperature of 350°F (175°C).

Carefully lower one donut at a time into the hot oil and fry until light golden brown on both sides. Allow the oil temperature to recover between batches. Transfer fried donuts to a cooling rack or paper towel-lined plate to cool slightly before filling.

Insert a Wilton 12 piping tip into a piping bag filled with the prepared pastry cream. Use a sharp knife to pierce each donut halfway through, then insert the tip and squeeze in the filling. Repeat for all donuts.

To make the glaze, combine the chocolate and heavy cream in a microwave-safe bowl. Heat in 20-second intervals, stirring between each, until the mixture is smooth. Dip the top of each filled donut into the glaze and return them to the rack to set.