Place rice in fine-mesh strainer and rinse under running water until water running through rice is clear, about 1½ minutes, swishing rice occasionally with your hand. Drain rice well.
Combine rice and 2½ cups water in large saucepan and bring to boil over high heat. Cover, reduce heat to low, and simmer for 20 minutes. Remove rice from heat and let stand, covered, for 10 minutes.
Heat oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add onion and cook until softened, 3 to 5 minutes. Add beef and cook, using wooden spoon to break meat into pieces, until beef is no longer pink, 3 to 5 minutes. Stir in taco seasoning and cook until fragrant, about 30 seconds. Stir in ketchup, mirin, soy sauce, instant dashi, and remaining 1 cup water; bring to boil; and cook until liquid is slightly thickened, 3 to 5 minutes.
Gently fluff rice with fork. Top individual portions of rice with beef; Monterey Jack; lettuce; avocado, if using; and salsa (in that order), and serve with lime wedges.
