**Marinate the Beef:** In a medium bowl, combine the thinly sliced beef with 1/4 cup soy sauce, 1 tablespoon cornstarch, and 1 teaspoon sesame oil. Toss well to coat. Let it marinate for at least 15-20 minutes at room temperature, or up to 30 minutes in the refrigerator.
**Prepare the Coating:** In another bowl, whisk together 1/2 cup cornstarch, 1/4 cup all-purpose flour, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Add the marinated beef and toss until each piece is thoroughly coated. Shake off any excess.
**Fry the Beef:** Heat about 1-2 cups of vegetable oil in a wok or large, deep skillet over medium-high heat until it shimmers (around 350°F/175°C). Carefully add the coated beef in batches, making sure not to overcrowd the pan. Fry for 2-3 minutes per batch, until golden brown and crispy. Use a slotted spoon to transfer the fried beef to a wire rack set over a baking sheet to drain.
**Make the Sauce:** Pour out most of the frying oil, leaving about 1 tablespoon in the wok or skillet. Reduce the heat to medium. Add the minced garlic and grated ginger and stir-fry for about 30 seconds until fragrant. In a small bowl, whisk together 1/2 cup soy sauce, hoisin sauce, water, rice vinegar, brown sugar, sriracha, and 1 teaspoon cornstarch until smooth.
**Combine and Thicken:** Pour the sauce mixture into the wok with the garlic and ginger. Bring to a simmer, stirring constantly, until the sauce thickens, about 1-2 minutes. Return the fried beef to the wok and toss quickly to coat each piece evenly in the glossy sauce. Be careful not to overcook the beef at this stage, as it can become tough.
**Serve:** Immediately transfer the Beijing Beef to a serving platter. Garnish generously with sliced scallions and toasted sesame seeds. Serve hot.