Fill a medium bowl halfway with ice, then cover ice with water and set aside.
Gently lower 6 large eggs into a large saucepan of boiling water.
When water returns to a gentle boil, cook 7 minutes.
Using a slotted spoon, transfer eggs to ice bath and let cool 2 minutes (eggs may still be a little warm).
Remove eggs from ice bath and peel.
Meanwhile, bring 5 garlic cloves, peeled, 3 dried chiles de árbol or 1 tsp. crushed red pepper flakes, ¾ cup soy sauce, 3 Tbsp. mirin, 2 Tbsp. unseasoned rice vinegar, and 2 cups water to a boil in a medium saucepan.
Reduce heat; simmer 5 minutes.
Remove from heat and add peeled eggs.
Let sit at room temperature at least 1 hour.
To serve, drain eggs, quarter, and sprinkle with toasted sesame seeds (if using).
