Preheat oven to 425˚F.
For filling: Melt butter in a medium saucepan over medium-high heat.
Add onions, carrot and celery and sauté for 3 to 4 minutes. Add thyme and season with salt and pepper. Reduce heat to medium and stir in flour and cook for 2 minutes. Stir in stock, followed by milk and continue to stir until mixture thickens enough to coat the back of a wooden spoon. Fold in chicken and peas, adjust seasonings and set aside to allow mixture to cool.
For dough: Place flour, baking powder and salt into a food processor and pulse 3 times. Add butter and cream cheese and continue to pulse until the mixture begins to come together. Add water and vinegar and continue to pulse until smooth dough forms. Divide dough into 2 flat discs, wrap in plastic wrap and refrigerate for 30 minutes.
To assemble: Roll chilled dough out onto a lightly floured surface into a 15” x 24” rectangle.
Cut out 3, 5”x 8” rectangles and brush the surface of each with the beaten egg. Place ¼ cup of the filling mixture into the bottom half of each rectangle (leaving a ¼ inch border).
Fold the top half of the rectangle-cut dough over the filling and gently press around the edges, getting rid of any air pockets. Using the back of a fork, seal the open edges. Gently score the top of each hand pie and brush with egg wash. Place them onto a parchment lined baking sheet.
Repeat steps 5-7 with the remaining dough and filling.
Bake for 18 to 22 minutes or until the hand pies are golden brown.
Allow hand pies to cool, about 10 minutes, before serving.