Make the sauce: combine the sauce ingredients in a bowl; set aside.
Make the stir-fry: Toss the steak with soy sauce; heat 2 teaspoons oil in a 12-inch nonstick skillet over high heat until just smoking.
Add in beef; cook, stirring occasionally and breaking up clumps, until lightly browned, about 3 minutes; transfer beef to clean bowl.
Add 1 more tablespoon oil to the pan and return to high heat until shimmering; add in broccoli and water to pan; cover, and cook until bright green and slightly tender, about 2 minutes.
Remove lid, add in bell pepper and water chestnuts; continue to cook until vegetables are tender, about 3 minutes.
Clear center of pan and add remaining 1 teaspoon oil, garlic, and ginger; cook, mashing garlic mixture into pan with back of spatula, until fragrant, about 30 seconds.
Stir in cooked beef; whisk Orange-Sesame Sauce to recombine; add to pan, and bring to a simmer.
Cook sauce until thickened, 1-2 minutes; serve immediately.