Toss the beef with 1 tsp. each of soy sauce and sesame oil and 1/4 tsp. salt. In a small bowl, mix the remaining Tbs. each of soy sauce and sesame oil with the ketchup, vinegar, sugar, chili sauce, and half of the sesame seeds.
Heat 1-1/2 Tbs. oil in a large (12-inch) skillet or wok over medium-high heat until shimmering. Add the beef and cook, stirring occasionally, until it loses its raw color and browns in places, about 2 to 3 minutes. Transfer to a large plate. Cook the ginger with the remaining 1-1/2 Tbs. oil until it sizzles steadily and starts to brown lightly around the edges, about 1 minute. Add the snap peas, sprinkle with 1/4 tsp. salt, and cook, stirring, until they turn bright green and start to brown in places, 1 to 2 minutes. Add 1/3 cup water and cook, stirring, until about half of the liquid cooks off and the peas start to soften, about 1 minute. Add the soy sauce mixture and beef, and cook, stirring, for a couple minutes until the mixture heats through and coats the peas and beef. Whisk the cornstarch with 1/4 cup water; add to the beef, and cook, stirring, until the sauce thickens, about 1 minute. Sprinkle with the remaining tsp. sesame seeds, and serve.