Toss the steak with 1 tablespoon soy sauce and 1 teaspoon cornstarch in a large bowl. Combine the cucumber and celery in a separate bowl; set aside.
Stir the black bean sauce with the remaining 1 tablespoon soy sauce and 1 teaspoon cornstarch, the cherry pepper brine and 1/4 cup water in a small bowl; set aside.
Heat 1 tablespoon vegetable oil in a large nonstick skillet over high heat. Add the cucumber-celery mixture and cook, undisturbed, 1 minute. Toss and cook, stirring occasionally, until crisp-tender, 1 to 2 minutes. Transfer to a bowl.
Heat the remaining 1 tablespoon oil in the same skillet. Add the steak in a single layer. Cook until browned on the bottom, about 1 minute. Toss and continue cooking, stirring, until just a few pink spots remain, 1 more minute. Add the garlic, ginger and peppercorns and cook, stirring, until the meat is cooked through, 1 to 2 more minutes. Add the black bean sauce mixture and cherry peppers and bring to a boil. Cook until glossy, about 1 minute. Toss in the cucumbers and celery.
Serve the stir-fry over rice. Top with celery leaves.