In the bowl of a stand mixer fitted with the dough hook, combine the active sourdough starter, warm milk, flour, eggs, salt, and sugar. Note: If your kitchen runs cold and you want this to ferment overnight, keep the milk cold.

Mix on low speed until a shaggy dough forms.

With the mixer running on low, add the softened butter one tablespoon at a time, allowing each addition to fully incorporate before adding more. Scrape down the sides of the bowl as needed.

Increase the mixer speed to medium-high and knead for 7–10 minutes, or until the dough becomes smooth, elastic, and begins pulling away from the sides of the bowl.

Cover the bowl and let the dough ferment at room temperature for 5–8 hours, or up to 10 hours in a cooler kitchen.

Turn the dough onto a lightly floured surface. Divide it into 12 equal portions, about 75 grams each.

Roll each piece into a smooth ball. Flatten each dough ball into a circle approximately 6 inches (15 cm) in diameter.

Place ½ slice of Swiss cheese in the center, followed by 2–3 slices of ham, then top with the remaining ½ slice of Swiss cheese.

Bring the edges of the dough up and over the filling, pinching them together tightly to completely seal the pocket.

Turn the seam-side down and gently roll it into a smooth, round ball. Place each pocket onto a parchment-lined baking sheet about an inch or two apart.

Cover the baking sheet loosely with greased plastic wrap. Allow the pockets to rise for 1–4 hours, or until noticeably puffy.

Preheat the oven to 350°F (177°C). In a small bowl, whisk together the melted butter, Dijon mustard, Worcestershire sauce, and poppy seeds until well combined.

Brush the mixture generously over the tops of each pocket just before baking.

Bake for 28–32 minutes, or until the pockets are deep golden brown and the internal temperature reaches 200–205°F (93–96°C).

Allow the pockets to cool for about 10 minutes before serving.