Melt 1 tablespoon butter in a small saucepan over low to medium heat. Once melted, add half of the 1/3 cup milk (approximately 2-3 tablespoons) and stir to combine.
Add 2 teaspoons cornstarch to the remaining milk and stir until completely dissolved. This prevents lumps from forming in your cheese dip.
Pour the cornstarch mixture into the saucepan. Add 1 teaspoon Worcestershire sauce, 1/2 teaspoon garlic powder, and a pinch of salt. Stir continuously until the mixture is smooth and begins to thicken slightly, about 1-2 minutes.
Remove the saucepan from heat and add 4 ounces of shredded cheddar cheese and 1/3 cup Greek yogurt. Stir until the ingredients are well combined.Return the pot to the stovetop over low heat. Stir continuously until the cheese is completely melted and the dip is smooth, about 1-2 minutes. Be careful not to let the mixture simmer or boil, as this can cause the Greek yogurt to separate.Transfer your cheese dip to a serving bowl and enjoy while warm. Serve with your favorite dippers like veggies, pretzels, or chips.