Perfect Yeast Doughnuts

Name: Perfect Yeast Doughnuts
Prep time: 30 min
Cook time: 15 min
Total time: 45 min
Cuisine: American
Ingredients: 6 Tbsp water (lukewarm); 5 oz buttermilk (at room temperature); 1 egg (at room temperature); 2 oz butter (melted); 16 oz all-purpose flour ((or bread flour)); 2 oz sugar; 1 tsp salt; 1 ½ tsp quick-rise yeast ((or regular dried yeast) ); 16 oz olive oil (for frying); 4 oz sugar ((1/2 cup or more as needed for coating the doughnuts)); jam, chocolate hazelnut spread, and or whipped cream for filling, if desired ((various amounts as needed))