Prepare rough puff pastry by combining flour and salt, cutting in cold butter until small chunks remain, then gradually adding ice water to form a shaggy dough.
Shape dough into a rectangle, roll, and fold like a book, repeat rolling and folding twice more. Wrap and refrigerate for at least 1 hour.
Make pie dough by mixing flour and salt, cutting in cold butter until coarse crumbs form, adding cold water gradually and forming a disc. Wrap and chill for at least 1 hour.
Tie thyme, parsley, and bay leaf. Season beef cubes with salt and pepper.
Heat 2 tablespoons olive oil in a Dutch oven over medium-high heat, sear beef batches until browned, about 8 minutes each. Set aside.
Add remaining olive oil to pot, sauté onion, carrots, and garlic until fragrant and lightly browned.
Return beef to pot, add 2 1/2 cups beef broth, coffee, chocolate, soy sauce, Worcestershire sauce, steak sauce, and the tied herbs.
Simmer covered on low heat for 2 1/2 hours, stirring occasionally. Remove herbs.
Mix cornstarch with remaining 1/2 cup broth, stir into stew to thicken for 5 minutes. Stir in peas, adjust seasoning, and cool completely.
Boil sweet potatoes in salted water until tender, drain and mash with butter, honey, salt, and pepper. Set aside to cool.
Preheat oven to 400°F and grease muffin tin. Roll pie dough to 1/4-inch thickness, cut 4-inch rounds, and line muffin cups with overhang.
Prick crust bottoms, line with foil and weights. Bake 15 minutes, remove weights, bake 5 more minutes.
Brush crusts with egg white and bake 2 to 3 minutes to seal. Cool completely.
Fill each crust with a tablespoon of sweet potato mash then beef stew almost to the top.
Roll rough puff pastry to 1/4-inch thickness, cut rounds to fit mini pies. Brush crust edges with egg white, place lids on top, and seal.
Brush tops with egg yolk mixed with water and cut small slits for steam.
Reduce oven to 375°F and bake pies for 20 to 25 minutes until puffed and golden.
Let pies rest 5 to 10 minutes before serving warm.