Activate the yeast by dissolving 2¼ teaspoons of active dry yeast in ¾ cup of warm milk (about 110°F/43°C) with a small portion of the ¼ cup granulated sugar. Allow the mixture to sit for 5-10 minutes until foamy.

In a large bowl, combine the remaining sugar, 3 tablespoons softened butter, 2 large egg yolks, 1 teaspoon vanilla extract, 2½ cups all-purpose flour, and ½ teaspoon salt. Mix until a soft dough forms, then turn it out onto a floured surface and knead for 5-6 minutes until smooth and elastic.

Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place until doubled in size (about 1 hour).

Meanwhile, prepare the pastry cream. In a saucepan, heat 2 cups whole milk with ½ cup granulated sugar. In a separate bowl, whisk together 4 egg yolks with ¼ cup cornstarch. Temper the egg mixture by slowly adding a bit of the hot milk, then combine back in the saucepan. Cook over medium heat until the mixture thickens. Off the heat, stir in 2 tablespoons unsalted butter and 1 teaspoon vanilla extract, then chill completely.

Once the dough has risen, roll it out to about ½-inch thickness and cut into rounds. Fry the dough rounds in vegetable oil until golden brown on each side (approximately 1-2 minutes per side). Allow the donuts to cool.

Using a piping bag, fill each cooled donut with the chilled pastry cream.

Prepare the chocolate glaze by placing 4 ounces of chopped semi-sweet chocolate in a heat-safe bowl. Heat ½ cup heavy cream until just simmering, then pour it over the chocolate along with 1 tablespoon unsalted butter. Let it sit for a minute before stirring until smooth and glossy.

Dip the top of each filled donut into the warm chocolate glaze and set aside to allow the glaze to set. Enjoy your homemade Boston Cream Donuts!