Preheat your oven to 350°F (175°C) and grease a 9x5-inch loaf pan with butter or cooking spray, then dust it with flour.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large mixing bowl, cream together the softened butter and granulated sugar using an electric mixer on medium speed for 3-4 minutes until light and fluffy.
Add the eggs one at a time, mixing well after each addition. Then mix in the key lime juice, key lime zest, and vanilla extract until well combined.
Gradually add the flour mixture to the wet ingredients, alternating with the sour cream, starting and ending with the flour mixture. Mix until just combined.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 55-65 minutes, checking for doneness with a toothpick.
Let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
For the glaze, combine powdered sugar, key lime juice, and key lime zest in a small bowl and whisk until smooth.
Once the cake is completely cooled, drizzle the glaze over the top and allow it to drip down the sides.