In a small saucepan, whisk together the brown sugar, soy sauce, garlic, ginger, and sesame oil. Bring to a boil and simmer until sugar has completely dissolved. Slowly whisk in cornstarch slurry into the mixture until thickened. Simmer for about 2 minutes. Remove from heat.
Let the remaining sauce cool then add raw shrimp. Mix, coat, and marinate shrimp in the glaze for about 10-15 minutes.
Skewer shrimp and leek pieces alternately onto wooden skewers.
Grill over high heat, turning once until shrimp is done, about 5-10 minutes depending on the size of the shrimp.
Brush the top of the cooked shrimp with more of the teriyaki sauce.