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These Texas-style pigs in a blanket would make for a great on-the-go breakfast, but could also be served as a crowd-pleasing brunch dish. Get the recipe for sausage kolaches.
Stir together milk and butter in a small saucepan over medium until butter is melted. Remove from heat; let cool, 12 to 15 minutes.
Stir together warm water, yeast, and 1 tablespoon sugar in a small bowl. Let stand until foamy, about 5 minutes.
In the bowl of a stand mixer with a dough hook attachment, beat together milk mixture, yeast mixture, flour, oil, kosher salt, 2 eggs, and remaining 3 tablespoons sugar on medium speed until smooth and elastic, about 7 minutes (dough will stick to the bottom of bowl but pull away from sides). Transfer dough to a large bowl lightly greased with canola oil. Cover with plastic wrap or a clean kitchen towel, and let rise at room temperature until nearly doubled in size, about 1 hour. Preheat oven to 350°F.
Whisk together remaining egg and 1 tablespoon water in a small bowl until combined. Punch dough down; transfer to a lightly floured surface. Divide dough into 12 equal pieces. Form each piece into a 4-inch round.
Brush edges with egg mixture. Place 1 piece of sausage in center of each round. Top each with 1 slice of cheese and 2 or 3 jalapeño slices. Lift sides of dough over sausage mixture, and pinch seam to seal. Place, seam side up, about 1 inch apart on a parchment-lined large baking sheet. Brush with remaining egg mixture. Top with more jalapeño slices and shredded Cheddar cheese.
Bake until golden brown, 20 to 25 minutes. Let cool 10 minutes before serving.