Warm the milk (about 100–110°F) and dissolve the yeast with a pinch of the sugar. Let it bloom for 5–7 minutes until foamy.

In a large bowl, whisk together the flour, salt, and remaining sugar. Add the bloomed yeast, softened butter, and eggs. Mix until a soft dough forms.

Transfer the dough to a lightly oiled bowl, cover with a clean towel, and let it rise in a warm place until doubled in size, about 1 to 1½ hours.

While dough rises, make the custard. In a saucepan, gently heat 2 cups whole milk until just warm.

In a bowl, whisk together egg yolks, 1/2 cup sugar, and cornstarch until pale and smooth.

Temper the egg mixture by slowly ladling a few tablespoons of warm milk into the yolks while whisking. Then pour the tempered egg mixture back into the saucepan with the remaining milk.

Cook the custard over medium-low heat, whisking constantly, until it thickens and coats the back of a spoon. Remove from heat and stir in 1 tsp vanilla extract.

Transfer to a shallow dish, cover with plastic pressed to the surface, and chill until fully set.

Once dough has doubled, gently punch it down and turn it out onto a floured surface. Divide into golf-ball sized pieces (about 1.5–2 inches). Cover and let rest 15 minutes.

Roll each piece into a smooth ball. Heat vegetable oil in a deep pot to 350°F (175°C).

Fry bombs a few at a time, turning gently, until golden brown on all sides — about 2–3 minutes per side. Drain on paper towels.

Using a piping bag fitted with a long skinny tip (or a skewer and spoon), fill each warm bomb with chilled custard.