Start by preheating your oven to 450°F and lining a large baking sheet with parchment paper or foil. While the oven heats, prepare all your ingredients: mince 7 garlic cloves and 5 additional garlic cloves (keeping them separate since they're used in different components), grate 2.5 inches of fresh ginger and measure out 2.5 tablespoons more ginger for the sauce, thinly slice 4 green onions on the diagonal, and cut 1 head of broccoli into 1-inch florets. I always prep my aromatics this way so there's no scrambling once cooking begins.
In a large bowl, combine 2 lb ground beef with the minced garlic and ginger from Step 1 (7 cloves garlic, 2.5 inches ginger), 4 green onions, salt, and pepper. Mix gently with your hands until just combined—overmixing makes tough meatballs. Roll the mixture into 1.5-inch balls and place them on one half of your prepared baking sheet. On the other half, toss broccoli florets with 1 tbsp olive oil, salt, and pepper. Bake everything together for 15 minutes until the meatballs are cooked through and broccoli is starting to char.
While the meatballs and broccoli bake, heat 1 tbsp vegetable oil in a large saucepan over medium-high heat. Add the remaining 5 minced garlic cloves and 2.5 tbsp ginger from Step 1, stirring constantly for about 30 seconds until fragrant. Pour in 1 cup soy sauce, 1 cup brown sugar, 2/3 cup water, 1 tbsp rice wine vinegar, 3/4 tsp red pepper flakes, and 1/2 tsp sesame oil. Bring to a simmer and let cook for 8-10 minutes to allow the flavors to meld together. I find that simmering the sauce before thickening it helps develop much deeper, more complex flavors.
In a small bowl, dissolve 2 tbsp cornstarch in 2 tbsp cold water, stirring until there are no lumps—this prevents the sauce from becoming grainy. Pour the cornstarch mixture into the simmering sauce from Step 3, stirring constantly until the sauce thickens to a glossy consistency that coats the back of a spoon, about 1-2 minutes. Once the meatballs finish baking in Step 2, carefully transfer them into the sauce and gently stir to coat evenly.
Arrange rice on a serving platter or individual bowls. Top with the Mongolian beef meatballs and their sauce from Step 4, then arrange the roasted broccoli from Step 2 alongside. Scatter the sliced green onions from Step 1 over the top and finish with a generous sprinkle of sesame seeds. Serve immediately while the meatballs and sauce are still warm.