Preheat your oven to 350°F. Grease an 8-inch loaf pan well, or line it with parchment paper, leaving some overhang to make removing the bread easier.
In a small bowl, stir together the granulated sugar, brown sugar, and cinnamon until evenly combined. Set aside.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, and granulated sugar.
In a separate bowl, whisk together the milk, melted butter, vegetable oil, Greek yogurt or sour cream, egg, and vanilla extract. Make sure the melted butter has cooled slightly before adding it.
Pour the wet ingredients into the bowl with the dry ingredients. Gently stir with a spatula or wooden spoon just until everything is combined and no large streaks of flour remain. Do not overmix. The batter will be thick.
Spoon half of the batter into the prepared loaf pan and spread it into an even layer.
Sprinkle about two-thirds of the cinnamon mixture evenly over the batter.
Carefully spoon the remaining batter over the cinnamon layer and spread it gently into an even layer. Sprinkle the remaining cinnamon mixture over the top.
Insert a butter knife about halfway into the batter and gently make a few swirling motions through the loaf. Don't over-swirl—you want visible ribbons of cinnamon throughout the bread.
Bake for 50–65 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. If the top begins browning too quickly, loosely cover the loaf with aluminum foil during the last 15–20 minutes.
Allow the bread to cool in the pan for about 15 minutes, then carefully transfer it to a wire rack to finish cooling.
While the bread cools, whisk together the powdered sugar, 2 tablespoons of milk, vanilla extract, and salt. Add additional milk, a teaspoon at a time, until the glaze reaches your desired consistency.
Once the bread has cooled, drizzle the vanilla glaze over the top. Slice and serve!