In a medium saucepan, melt the butter on medium-low and add the a jalapeños. While stirring occasionally, cook until softened and fragrant, about 5 minutes. Add the garlic and cook for 30 more seconds. Remove the jalapeños and garlic from the pot.
Pour into the pot the milk and water, add the salt, then turn the heat to high. When the liquid comes to a boil, turn the heat down to low, add the grits, and stir until thick and creamy, about 5-8 minutes.
After the grits are done, stir in the cheese, jalapeños, garlic, and stir until the cheese has melted. Taste and add more salt if needed.