Drain chickpeas and reserve the chickpea brine, or aquafaba and set aside.
In the food processor, add the garlic, lemon juice, 3-4 tbsp aquafaba and tahini. Process for about a minute. This should help to break down the garlic and also whip up the tahini.
Add the gochujang and chickpeas and process again until mostly smooth, then stream in olive oil while processing.
Add ice cubes and process again until fully broken down and incorporated. This helps to slowly add air and moisture to the hummus. You can adjust the texture by adding additional olive oil, or cold water, as needed.
Once desired texture is achieved, taste and add salt as desired, and additional gochujang, if you'd like. Blend to incorporate.
To serve, transfer to a bowl and use the back of a spoon to apply light pressure while rotating the bowl with your other hand. This will create a nice groove in the hummus so you can drizzle in toasted sesame seeds. Top with desired garnish and enjoy.