Preheat oven to 400F (205C).
Combine flour, baking powder, sugar, and salt in the basin of a food processor². Scatter butter over the top of the mixture and pulse briefly to combine (butter pieces should still be visible, mixture should resemble coarse, pebbly crumbs). Add milk and pulse very briefly until just combined and mixture is clumping together.
Transfer to a piece of cling wrap and pat into a 1” thick rectangle (flour your hands if the dough is sticky), and then cover with cling wrap and refrigerate until filling is prepared.
Melt butter in a large pot or dutch oven over medium heat (the pot you choose is the one you’ll be baking your pot pie in, make sure it’s big enough!).
Add chopped onion and cook until tender and translucent (about 4 minutes.
Sprinkle onion with with flour and whisk until smooth. Stir in salt, pepper, and spices (paprika, mustard, and thyme) until well-combined.
Gradually stir in chicken broth and heavy cream. Add potatoes, carrot, and mixed veggies and bring contents to a boil over medium heat, stirring frequently until liquid has thickened. Continue to boil until potatoes and carrots are tender when pierced with a fork.
Remove from heat and stir in chicken. Remove biscuit dough from fridge and cut into 6-8 pieces (you can use a biscuit cutter or just cut the dough into rectangles with a knife).
Distribute biscuits evenly over the surface of pot pie, leaving a little space between biscuits. If desired, prepare egg wash by whisking together egg and water and use a pastry brush to brush the tops of the biscuits.
Transfer pot pie to 400F (205C) oven and bake for 25 minutes or until biscuits are beginning to turn a light golden brown (if you skipped the egg wash it will be a bit tougher to tell that they’re done as they stay pale) and cooked through. I’ll usually pierce the side of a biscuit with a knife to make sure it’s not gooey.
Serve and enjoy!