In the bowl of a stand mixer fitted with the dough hook (or in a large mixing bowl), whisk together 3 1/2 cups all-purpose flour, 2 tsp instant yeast, 4 tbs granulated sugar, and 1 tsp fine salt until evenly distributed.

Mix wet ingredients

In a separate measuring cup or bowl, whisk together 1 cup warmed whole milk (100–110°F / 38–43°C), 1/2 cup additional warmed milk, and 1 large egg until smooth. Add the wet mixture to the dry ingredients.

Initial mixing

Start the mixer on low and mix until flour is mostly hydrated and a shaggy dough forms, about 2–3 minutes. If mixing by hand, stir with a wooden spoon until combined.

Knead and add butter

Increase mixer speed to medium and knead while adding the 4 tbs softened unsalted butter, a piece at a time. Continue kneading until the dough is smooth, elastic, and slightly tacky but not sticky, about 8–10 minutes by mixer or 10–14 minutes by hand. If dough feels dry, add up to 1–2 tbs more warmed milk (add sparingly). If too sticky, dust with up to 1–2 tbs extra flour.

First rise

Shape dough into a ball and place in a lightly greased bowl, turning once to coat. Cover with plastic wrap or a damp towel and let rise in a warm draft-free spot until doubled in size, about 60–75 minutes depending on room temperature.

Punch down and divide

Gently deflate the risen dough and turn it out onto a lightly floured work surface. Divide the dough into 12 equal pieces (about 65–75 g / 2.3–2.6 oz each). Cover pieces with a towel while shaping to prevent drying.

Shape pillows

For plain pillows: flatten each piece into a small disc, fold edges to the center, seal, and roll seam-side down into a smooth ball. For filled pillows: flatten each piece into a 3–4 inch disc, place about 1 tablespoon sweetened condensed milk OR 1 tablespoon softened cream cheese OR 1 tablespoon jam in the center, gather edges up and pinch to seal, then roll seam-side down into a smooth ball. Ensure seams are well sealed so filling does not leak.

Second rise on tray

Place shaped buns seam-side down on a parchment-lined baking tray, spacing them 2 inches apart (for pull-apart, place closer). Cover loosely with plastic wrap or a damp towel and let rise until puffy and nearly doubled, about 35–45 minutes.

Milk Brush & Bake

Preheat oven

About 15 minutes before the end of the second rise, preheat the oven to 350°F (175°C). Position a rack in the center of the oven.

Brush with milk mixture

Whisk together 2 tbs whole milk and 1/2 tsp vanilla extract (and 1 tbs melted butter if using). Gently brush the tops of the risen buns with the milk mixture, taking care not to deflate them.

Bake

Bake the buns in the preheated oven for 14–18 minutes, or until the tops are golden brown and the internal temperature reaches about 190°F (88°C). Rotate the tray halfway through baking if your oven has hot spots.

Finish and glaze

Remove buns from the oven and immediately brush with a little melted butter (optional) for a softer, shiny crust. Transfer to a cooling rack. If desired, once slightly cooled, dust very lightly with 1 tbs powdered sugar or brush again with a little sweetened condensed milk for extra sheen and sweetness.

Serve

Serve the milk pillow breads warm or at room temperature. If filled, allow buns to cool slightly so filling firms up a bit before serving to avoid leakage.