Preheat the oven to 350°F. Grease a 9 x 9" baking dish and line with parchment paper, leaving a slight over-hang so (hopefully) you can lift it out easily
In a medium bowl, whisk together the milk, oil, egg, tahini, and vanilla extract.
In a large bowl, sift together the flour, baking powder, and salt. Add the sugar, coconut, and cinnamon. Stir to combine.
Gently whisk the wet ingredients into the dry, then add the grated carrot.
Bake for 30-35 minutes, or until the cake springs back when pressed and a toothpick inserted into the center comes out clean. Let cool slightly, then gently lift out (by the parchment paper) and onto a rack to cool completely.