Heat olive oil in a large pot over medium low heat. Add garlic and cook until fragrant, about 2-3 minutes. Add grits, vegetable broth and milk and cook according to package instructions. Stir in chipotle pepper and goat cheese.
In a small bowl, whisk together Greek yogurt and cornstarch. Add a small amount of the grits to the Greek yogurt to temper. Stir to combine. Do this 2-3 more times, then stir Greek yogurt into the pot with your grits.
Serve immediately. Drizzle with extra chipotle sauce if desired.