Mix Dry Ingredients:

In a bowl, combine bread flour, sugar, yeast, and salt.

Add Wet Ingredients:

Pour in milk, melted butter, and vanilla extract; stir until a soft, sticky dough forms.

Knead Dough:

Knead on an unfloured surface for roughly 10 minutes until smooth, supple, and elastic. The dough should remain slightly sticky but not wet. If overly wet, dust with a small amount of extra flour, but avoid overdoing it to prevent dry doughnuts.

First Rise:

Transfer dough to a lightly oiled bowl, cover, and let rise until doubled—about 1 1/2 to 2 hours in a warm area or overnight in the refrigerator.

Deflate Dough:

Deflate the risen dough and knead briefly to eliminate air pockets.

Divide Dough:

Split into 8 equal portions (use a scale for precision).

Shape Balls:

On a surface dusted with flour, form each piece into a ball: pull edges to the center and pinch to seal, then flip over, cup with your hand, and roll into a smooth sphere.

Flatten Discs:

Press each ball into a disc roughly 1 1/2 to 2 cm thick. Repeat with remaining pieces. (For thicker doughnuts, omit flattening.)

Second Rise:

Arrange discs on a parchment-lined baking sheet, cover loosely, and let rise until puffy, about 45 minutes. The dough is ready when a gentle finger press leaves an impression that slowly rebounds. If it springs back quickly, extend proofing; if it collapses or fails to spring back, the dough is over-proofed—punch down, reshape, and re-proof.

Preheat Oil:

Shortly before proofing ends, preheat deep fryer to 340°F (170°C). Prepare a shallow dish with caster sugar and a plate lined with paper towels.

Fry Doughnuts:

Fry doughnuts in batches of two. Gently slide them into the hot oil; they are fragile, so handle minimally. Cook for 2 1/2 minutes (use a timer), then flip and fry another 2 1/2 minutes until deep golden brown.

Drain and Sugar:

Retrieve with a slotted spoon and drain on paper towels. While still warm, roll each doughnut in caster sugar.

Pierce Doughnuts:

Pierce the side of each doughnut with a skewer or small sharp knife, then wiggle to create an interior cavity.

Fill Piping Bag:

Fill a piping bag fitted with a medium round nozzle (or a syringe) with jam.

Inject Jam:

Insert the nozzle into the hole and inject a generous amount of jam. Serve immediately.