In a large bowl, stir together 1 1/2 cups cheddar, mozzarella, cream cheese, Dijon, chives, garlic powder, and beer and season with salt and pepper.
Halve each biscuit and roll into a ball, then slice an X across the top.
In a small saucepan, bring 2 cups water and baking soda to a boil and whisk to dissolve.
Immediately reduce heat to maintain a simmer.
Add biscuits in batches and cook until puffy, 30 seconds, then remove with a slotted spoon and transfer to a 10" or 12" ovenproof skillet, forming a ring along the inside edge.
Brush biscuits with egg wash and sprinkle with coarse salt.
Transfer dip to center of skillet and sprinkle with remaining 1/4 cup cheddar.
Bake until biscuits are golden and dip is bubbly, 33 to 35 minutes.