In a stand mixer bowl, combine all dough ingredients except the butter. Mix with a spatula until a shaggy dough forms.

Using the stand mixer fitted with the dough hook attachment, knead for 8 minutes on low–medium speed until the dough is elastic.

Add softened butter, 2 tablespoons at a time, kneading thoroughly after each addition. Once all the butter is added, knead for 8-10 minutes more, until the dough is very smooth, supple, and starts to pull away from the sides.

Grease your hands, shape the dough into a rough ball, then transfer it to a medium, lightly greased bowl. Cover and let rise in a warm place (75–80°F) for 1 ½ to 2 hours, or until almost doubled in size.

Line two sheet trays with parchment paper. Turn the risen dough out onto a lightly floured surface. Divide into 8 equal portions (about 4 oz each).

Using a rolling pin or your hands, flatten each piece into an oval or rectangular shape, just slightly wider than the sausage link.

Sprinkle about 2 tablespoons of shredded cheddar cheese down the center of each piece of dough. Place half a sausage link (or two mini links) on top.

Fold the dough over the sausage lengthwise, pinching the seam to seal. Then fold in the short edges, pinching to seal again. Gently roll the log to help seal and smooth the dough.

Place the sealed kolaches seam-side down on the prepared sheet trays, spacing them evenly apart. Cover loosely and let rise until noticeably puffy, about 1 hour.

Preheat the oven to 375°F (190°C). Brush each klobasnek with egg wash. If using, place a jalapeño slice in the center and press down gently. Sprinkle with everything bagel seasoning or poppy seeds, if desired.

Bake for 15–20 minutes, or until golden brown and the internal temperature of the dough reaches 190°F to 200°F. Rotate pans halfway through for even browning.