Begin by preparing the sauce: In a measuring cup or small mixing bowl, combine the brown sugar, soy sauce, rice vinegar, sesame oil, and red pepper flakes. Whisk until well-blended, then add the cornstarch and whisk again until smooth. Set aside.
In a large skillet or wok, heat the olive oil over medium-high heat until shimmering.
Add the ground beef to the skillet and season with kosher salt and freshly ground pepper. Cook, breaking up the meat with a spatula, until no longer pink and fully browned.
Introduce the diced bell pepper and shredded carrots to the skillet. Stir frequently and cook until they begin to soften, approximately 3 to 4 minutes.
Stir in the minced garlic and grated ginger, allowing them to cook for about 1 minute until aromatic.
Fold in the chopped water chestnuts, then pour the prepared sauce over the mixture. Stir continuously and bring to a gentle simmer. Cook until the sauce thickens, roughly 2 minutes.
Taste and adjust seasoning as needed, then stir in the chopped green onions just before removing from heat.
Spoon the warm filling into individual lettuce leaves. Garnish with sesame seeds and serve immediately.