In a large bowl, toss the beef cubes with chickpea flour.
Heat half of the oil in a Dutch oven over medium-high heat. Brown the floured meat in batches, adding remaining oil as necessary.
Return all the beef to the pan. Add stock, tomato sauce, coffee, oregano, salt, thyme, and pepper. Bring to a boil. Reduce heat and simmer for 1 hour.
Add vegetables and simmer for another hour or until potatoes and carrots are tender. Remove from heat and allow to cool. (Make ahead: Cover and refrigerate for up to two days.)
Preheat oven to 400°F.
Stir green beans into the beef pie filling.
Cover with gluten free pie crust, leaving about ½-inch overhang. Fold the edges under, and pinch pastry to the edges all the way around.
Beat the egg and brush it over the top of the crust.
Poke a few vent holes into the crust. Bake in the centre of the oven for 45 minutes or until hot and bubbly and pastry is golden.
The filling and pastry can each be made up to a couple days ahead and assembled just before baking. If you have one pot that is safe for both stovetop and oven, it's great for this recipe. Otherwise, start the filling on the stovetop and transfer it to an oven-safe casserole dish for baking.