Adjust the oven rack to the middle position and preheat to 475 degrees F (245 degrees C). Line a baking sheet with parchment paper.
In a food processor, pulse the 130 grams all-purpose flour, 15 grams evaporated cane sugar, 7.5 grams baking powder, 3 grams baking soda, and 3 grams salt to combine.
130 grams all-purpose flour, 15 grams evaporated cane sugar, 7.5 grams baking powder, 3 grams baking soda, 3 grams salt
Distribute the 28.5 grams cultured unsalted butter evenly over the flour and pulse 1 full second at a time until the mixture resembles gravel. Add the 30 grams white cheddar and pulse a few more times to break up the cheese, but be sure to leave some small chunks.
28.5 grams cultured unsalted butter, 30 grams white cheddar
Transfer this mixture to a bowl and stir in the 2 tablespoons chives.
2 tablespoons chives
Shake (or whisk) the ⅔ cup plain yogurt until it's thin enough to pour.
⅔ cup plain yogurt
Add the yogurt to the the dry ingredients and stir until just combined. It's okay if it's not 100% incorporated but be careful not to overmix.
Working quickly, put 4 small circles of batter down on the parchment paper and top each one with one of the 4 soft boiled eggs standing upright. Cover each egg with the remaining batter and place the pan into the pre-heated oven.
4 soft boiled eggs
Bake for 4-5 minutes and then turn down the heat to 400 degrees F (200 C) and bake until the biscuits are golden brown (about another 7-10 minutes).
Serve hot, or transfer to a wire rack to cool completely.