First bring a large pot of water to a boil. Very carefully, with a slotted spoon, lower the eggs one by one into the boiling water as to not crack the shell. Let eggs boil for 4 - 4½ minutes and remove again one by one with a slotted spoon into a bowl of ice water. Once eggs are cool enough to handle, peel the shell and add eggs back into ice bath (you may need to refill with cold water & more ice). Set aside peeled eggs until ready to use.
Preheat your oven to 450 degrees. In a large bowl add your flour, sugar, baking powder, baking soda, salt & cheese. Mix together. Add your heavy cream and milk. Fold until ingredients come together (this will be a little chunky in texture).
Next lay some parchment paper down on a large baking sheet. Using a spoon scoop about ¼ cup of dough onto paper. Using your thumb make an indentation large enough that will hold an egg. You're basically creating a nest here. Place your soft boiled egg carefully into nest on it's side (refer to pictures) and then take another scoop of dough (about ⅓ cup) into your hands and flatten it like a pancake (will be about 2-3" in diameter). You may need more or less dough here just depending on how nested your egg is to begin with.
Take your now disc shaped dough and place on top of egg (like a blanket.) Carefully pinch the top and bottom dough layer together, sealing the egg inside the dough. Refer to pictures.
Continue to do this until all of your dough is used up. I had some dough left over and was able to make a regular biscuit. Place egg biscuit in oven for about 13-15 minutes. You may check to see if biscuit is done by barely piercing it with a knife (do not want to pierce through to the egg) and if the knife is mostly clean when removed the biscuits are ready (it may be crumby, just not smeared with dough).
Remove immediately and serve warm!
Recipe by My Lavender Blues at https://mylavenderblues.com/soft-boiled-egg-in-a-cheddar-biscuit/