Salt and pepper the beef chunks. In batches, brown them in 2 tablespoons of olive oil in a large sauté pan over medium-high heat. Set aside.

Preheat the oven to 250°F.

In a large Dutch oven over medium-high heat, sauté the diced onion in 1 tablespoon of olive oil and 2 tablespoons of butter until translucent, 7 to 8 minutes.. Add the garlic and cook 1 minute longer. Add the beef and the port wine, consommé, tomato paste, and thyme. Bring to a boil, cover, transfer to the oven, and cook for 2 hours.

Meanwhile, blanch the carrots until fork-tender, 5 to 6 minutes, in a saucepan of lightly boiling water. Drain and set aside. In a sauté pan over medium-high heat, cook the mushrooms in 1 tablespoon olive oil and 2 tablespoons butter until lightly browned, 4 to 5 minutes. Set aside.

When you remove the Dutch oven from the oven, make a roux in a saucepan by melting 1 stick of butter over medium heat and then whisking in the flour for 2 to 3 minutes. Bring the stew to a boil on the stovetop and stir in the roux, continuing to stir until the sauce thickens. Reduce the heat to a simmer and stir in the mushrooms, carrots, and pearl onions. Simmer for 5 to 10 minutes, then turn off the heat. Add salt and pepper to taste.

Raise the oven temperature to 400°F. Meanwhile, spoon the beef mixture into a 3-quart baking dish or 2 deep-dish pie plates. Cover with the pie pastry, trimming and overlapping the dough to fit the dish. In a small bowl, beat together the egg yolk and water, then brush the over the dough. With a fork, punch a dozen or so holes all over the crust. Bake until the crust is golden brown, 20 to 25 minutes Leave at room temperature to settle for 5 to 10 minutes before using a large spoon to serve portions of crust and filling.