Remove cream cheese from the refrigerator and place it on the counter to soften about 20 minutes before you start cooking.
When you're ready to begin, preheat the oven to 400 degrees and remove pie crusts from the refrigerator to soften as directed on the box.
Add olive oil to a large skillet and heat it over medium heat until shimmering. Add onion and cook for two minutes.
Add broccoli florets, garlic, and crushed red pepper, then saute for about five more minutes, until broccoli is bright green and crisp-tender.
Meanwhile, combine cream cheese, cheddar cheese, chicken, sea salt, black pepper, paprika, and thyme in a large bowl, then stir in the broccoli once it is cooked.
Unroll the pie crusts and cut each into 4-8 equal wedges, so that you have 8-16 pieces total between the two crusts.
Spoon equal amounts of the chicken/broccoli mixture into the center of half of the pie crust wedges, and top each with a second matching wedge.
Fold the edges over on each and crimp them together so that the filling doesn't leak out, then arrange the hand pies on a rimmed baking sheet.
Beat one egg with 1 tsp water to make an egg wash. Brush each hand pie with the egg wash, and cut a couple of small slits in the top of each to let steam escape.
Bake for 20 minutes at 400 degrees, or until hand pies are golden brown.
I cut my pie crusts into quarters, which were big for one person -- I'd suggest going with sixths instead, and therefore am calling this a recipe that serves six. You can also cut the crusts into eighths to make 8 smaller hand pies, especially if you're serving kids.