Set your oven to 350°F to start warming. In a medium bowl, whisk together milk, egg, sugar, vanilla extract, melted butter, and Greek yogurt until smooth. In another bowl, mix together the flour, sea salt, baking soda, baking powder, and cinnamon. Add the dry mix into the wet ingredients gently and fold in the shredded carrots. Spoon or pipe the batter into a greased donut pan filling each cavity about two-thirds full. Bake for 9 to 12 minutes, or until a toothpick inserted comes out clean. While baking, beat cream cheese with softened butter using an electric mixer until creamy. Mix in vanilla and sea salt, then gradually add powdered sugar half a cup at a time until the frosting reaches your preferred sweetness and thickness. Let the donuts cool completely before applying the frosting. Keep them stored in an airtight container in the fridge for up to 4-5 days for best taste.