In a small saucepan, bring the rice and 1 1/2 cups water to a boil. Stir, lower the heat, cover and simmer for 18 minutes.
Meanwhile, in a large skillet, heat 1/2 tablespoon olive oil over medium heat. Add the portobello mushrooms, rounded side down, cover and cook until the liquid is released, 2 to 3 minutes. Season with salt and pepper, flip and cook, uncovered, until tender, about 2 minutes more. Transfer to a plate.
Cut the beef filet crosswise into 8 pieces and pound each one 1/3 inch thick. Season with salt and pepper. In a resealeable plastic bag, combine 4 beef slices and the flour; shake to coat. Transfer slices to a plate and repeat with the remaining beef.
In the same skillet, heat 1 1/2 tablespoons olive oil over medium-high heat. Add 4 beef slices and cook, turning once, until browned, 4 minutes total. Transfer to the plate with the portobellos, and repeat with the remaining 1/2 tablespoon olive oil and 4 beef slices.
In the same skillet, over medium heat, cook the shiitakes, shallots and scallions, stirring, until the mushrooms are softened, about 3 minutes. Pour in the brandy and simmer for 30 seconds, then add the beef broth and bring to a simmer. Add the beef and portobellos to the skillet and cook, turning, for 2 minutes for medium-rare.
Divide the rice among 4 serving plates and top each with 2 beef slices and a portobello. Simmer the sauce for 1 minute, remove from the heat, season with salt and pepper and stir in the yogurt. Spoon the sauce over the beef and portobellos.