Melt Butter: Place the butter in a small saucepan over low heat. Melt until fully liquid, about 3 minutes, then keep it warm for the hollandaise.
Add Yolks: Place the 3 egg yolks in a blender. Make sure only the yolks go in so the sauce turns thick and smooth.
Fill Ramekins: Pour ½ cup water into each microwave safe ramekin. The water should be deep enough to cover each egg.
Add Eggs: Crack 1 whole egg into each ramekin. Keep the yolk whole so the eggs poach neatly.
Microwave Eggs: Microwave the eggs until the whites are set and the yolks are still soft, about 45 to 60 seconds per ramekin. If microwaving more than one at a time, cook for about 1½ to 2 minutes total, checking often so the yolks do not overcook.
Season Hollandaise: Add 1 tablespoon lemon juice, kosher salt, and hot pepper sauce to the blender with the egg yolks.
Blend Sauce: Blend the yolk mixture for about 10 seconds. With the blender running, slowly pour in the warm melted butter and blend until the sauce is thick, smooth, and pale yellow, about 1 minute.
Cut Cheddar: Cut the extra sharp cheddar cheese into small cubes. Set it aside for the potato salad.
Prep Lemon: Zest the lemon with a microplane, then squeeze the juice. Use the remaining lemon juice later in the potato salad.
Chop & Cook Bacon: Chop the bacon into small bite size pieces so it cooks evenly and mixes well into the salad. Add the chopped bacon to a large skillet over medium heat. Cook, stirring often, until browned and crisp, about 5 to 7 minutes.
Add Peas and Potato Salad: Stir the fresh English peas into the skillet with the bacon. Cook over medium heat for 2 to 3 minutes, just until the peas turn bright green. Spoon the deli red potato salad into the skillet. Stir it into the bacon and peas until it loosens and warms through, about 3 to 4 minutes.
Add Lemon: Stir in the lemon zest and remaining lemon juice. Mix until the potato salad tastes bright and creamy.
Add Cheddar: Stir in the cubed cheddar cheese. Mix gently so the cheese stays in soft little chunks.
Fold in Arugula: Add the baby arugula and toss just until it starts to wilt, about 30 seconds. Remove the skillet from the heat.
Split Biscuits: Split the biscuits in half and place them on serving plates. Use one biscuit per serving.
Add Poached Eggs: Lift each poached egg from the water with a slotted spoon and let the extra water drain off. Place one egg on the bottom half of each biscuit.
Plate Potato Salad: Spoon the warm springtime potato salad onto each plate beside the biscuit and egg.
Sauce and Serve: Spoon the hollandaise over each poached egg. Add the biscuit tops on the side and serve right away.