Heat milk in a small saucepan over medium heat until it begins to bubble; remove from heat immediately. Stir in sugar, 1/4 cup butter, and salt until sugar is dissolved. Set aside to cool to room temperature.

Combine warm water and yeast in the large bowl of a stand mixer and stir until dissolved. Stir in 2 cups flour, cooled milk mixture, and eggs; beat using the dough hook attachment until smooth. Add remaining flour gradually until dough is elastic and slightly stiff, but not dry.

Turn the dough onto a floured board. Knead until smooth and very elastic. Brush lightly with melted butter, cover, and let rise in a warm place until doubled.

Cut sausages in half and pat dry. Thinly slice Cheddar cheese block into suitable sizes for filling.

Preheat oven to 350°F (175°C). Lightly grease a baking sheet.

Roll risen dough into a log, divide into 20 equal pieces. Flatten each piece into a circle or oval, add cheese and sausage, then roll dough tightly around the filling, sealing all seams.