Mix 3 eggs, 1 cup of milk (or 3/4 cup whole milk + 1/4 water), 1/2 cups sourdough starter, 1 cup of white flour, and 1/2 tsp. salt. Be sure all the ingredients are thoroughly incorporated, but don't overmix.
Mix in 1/4 cup shredded cheese and 1 Tbsp. chopped rosemary.
Cover and refrigerate overnight or at least six hours.
Remove the batter from the fridge (if you fermented it there) and bring to room temperature.
Add one teaspoon of beef tallow or olive oil to each well of the pudding/muffin tin. Preheat the oven and the popover/muffin pan with the oil to 425F/218C.
Evenly distribute the batter to each tin cup; fill each cup 3/4 full. Space the batter around the tin to allow for air circulation around each pudding/popover.
Bake at 425F/218C for 15 minutes, then reduce the heat to 350F/176C for another 15 minutes. If your oven runs hot, watch for burning.
Remove from the pan and place on a baking rack to set up for a few minutes. Serve warm.