Pour the water, milk, butter, and 1 teaspoon salt into a medium sauce pan. Heat mixture over medium-high heat until it begins to boil. Once it's boiling, very very slowly pour in the grits while whisking quickly for 2 minutes. Reduce heat to medium-low, cover, and let cook for 30 minutes, stirring occasionally.
While the grits cook, add olive oil to medium skillet and heat to medium. Add onion and cook until translucent, about 5 minutes. Add garlic and corn kernels and cook for another 5 minutes. Season with salt and pepper.
Add corn mixture to a blender and carefully blend mixture until it's pureed. Allow the steam to exit the blender after 10 seconds so it doesn't build up. Once the mixture is smooth, it is ready.
When the grits are cooked, add in the pureed corn mixture. Add goat cheese to grits, about 1 ounce at a time so that it can melt completely into grits. Serve immediately.