Sausage Kolaches

Name: Sausage Kolaches
Ingredients: 3/4 cup whole milk; 1/4 cup unsalted butter; 1/4 cup warm water (100°F to 105°F); 2 1/4 tsp. active dry yeast; 4 Tbsp. granulated sugar, divided; 3 1/2 cups all-purpose flour, plus more for surface; 2 Tbsp. canola oil, plus more for greasing bowl; 1 tsp. kosher salt; 3 large eggs, divided; 1 (16-oz.) pkg. smoked sausage (such as Conecuh), cut into 12 (4-inch) links, cooked and cooled; 1 (8-oz.) block sharp Cheddar cheese, cut into 12 slices; 2 jalapeños, thinly sliced; Shredded Cheddar cheese