Combine 2 3/4 cups flour and kosher salt in a large bowl. Cut lard into flour mixture until it resembles coarse bread crumbs. Add ice water, one tablespoon at a time, tossing to mix. Gather dough into a ball, divide it in half, and wrap each piece in plastic wrap. Refrigerate while you prepare the filling.

Mix 2 1/2 tablespoons flour, 1/2 teaspoon thyme, paprika, pepper, ginger, and allspice together in a bowl. Dredge steak pieces in seasoned flour and set aside.

Heat olive oil in a skillet over medium-high heat. Stir in seasoned steak and onion; cook and stir until onion has softened and turned translucent and steak is browned on all sides, about 10 minutes. Pour in beef broth and red wine; simmer until sauce thickens, about 20 minutes.

Roll out one pastry crust on a lightly floured surface to fit a 10-inch pie plate. Place crust into the pie plate, cover it loosely with plastic, and refrigerate. Roll out top crust for the pie and set it aside.

Stir potatoes and carrots into the skillet and simmer until tender, about 20 minutes. Remove from the heat and allow to cool slightly, about 10 minutes.

Preheat the oven to 400 degrees F (200 degrees C).

Transfer cooled beef mixture to the pastry-lined pie plate. Sprinkle with remaining 1/2 teaspoon thyme, then cover with the top crust and crimp the edges to seal. Cut vents in the crust or prick with a fork to allow steam to escape.