1. In a large mixing bowl, combine your active sourdough starter, warm milk, granulated sugar, salt, and one large egg. Whisk these ingredients together until well combined. The mixture should look slightly frothy from the starter.

2. Gradually add the melted and cooled butter, then slowly incorporate the all-purpose flour, one cup at a time, mixing with a wooden spoon or a stand mixer with a dough hook. If using instant yeast, add it with the first cup of flour. Mix until a shaggy dough forms.

3. Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or use a stand mixer with a dough hook on medium speed for 5 minutes. The dough should become smooth, elastic, and less sticky. It should pass the “windowpane test,” meaning you can stretch a small piece thin enough to see light through it without tearing.

4. Lightly grease a clean bowl with butter or oil. Place the kneaded dough into the bowl, turning it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 to 2 hours, or until it has nearly doubled in size. The dough should feel soft and airy.

5. Gently punch down the risen dough to release the air. Turn it out onto a lightly floured surface. Divide the dough into 12-16 equal pieces, depending on your desired slider bun size. Roll each piece into a smooth, tight ball. Arrange the dough balls on a parchment-lined baking sheet, leaving about 1/2 inch between them so they can kiss and form pull-apart buns.

6. Cover the baking sheet loosely with plastic wrap or a clean kitchen towel and let the buns rise again in a warm place for another 30-45 minutes, or until they look puffy and have increased in size by about 50%. Towards the end of this rise, preheat your oven to 375 F (190 C).

7. In a small bowl, whisk the remaining egg with a tablespoon of water to create an egg wash. Gently brush the tops of the risen buns with the egg wash. If desired, sprinkle with sesame seeds or everything bagel seasoning. Bake for 15-18 minutes, or until the buns are golden brown on top and sound hollow when tapped on the bottom.

8. Remove the baking sheet from the oven and transfer the buns to a wire rack to cool slightly. Serve warm and enjoy your delicious homemade sourdough slider buns!