COMBINE yogurt or sour cream, salt, pepper, lemon juice, and chopped herbs in a small bowl. Mix until smooth and set aside.
INSERT one piece of cheddar cheese into each olive and set aside.
HEAT 3 cups of oil (or 1 to 2 inches) in a high-sided pot to 350°F.
WHISK together 1 cup self-rising flour, cornstarch, baking powder, and cold beer until smooth in a medium bowl to make wet batter.
PLACE ¾ cup self-rising flour in a shallow bowl to make dry batter.
ROLL the stuffed olives in batches, in the dry batter to coat. Dip them into the wet batter, ensuring they are evenly coated. Use a fork to remove excess batter.
DROP the coated olives carefully into the hot oil in small batches. Fry until golden brown, then remove with a slotted spoon and place on a paper towel-lined plate to drain.
SERVE the fried olives with the prepared dipping sauce and hot honey or an additional sauce, if desired.
