Preheat the oven to 350 degrees F. Grease an 8 x 5-inch loaf pan. Line the bottom with parchment paper. Grease and flour the pan.
Sift together the flour, baking powder, and salt into a bowl. In another bowl, whisk together the yogurt, sugar, eggs and grapefruit zest. Slowly whisk the dry ingredients into the wet ingredients. With a rubber spatula, fold the vegetable oil into the batter, making sure it's all incorporated. Pour the batter into the prepared pan and bake for about 40-45 minutes, or until a cake tester placed in the center of the loaf comes out clean.
Meanwhile, to a small saucepan, add grapefruit juice, sugar, a splash or two of water and the thyme. Cook until the sugar dissolves and the mixture is clear. Set aside so the thyme can steep, about 30 minutes. Strain and set aside.
To make the glaze, add two tablespoons of the grapefruit/thyme syrup to a bowl. Sift in the confectioners' sugar and mix until smooth.
When the cake is done, allow it to cool in the pan for 10 minutes. Using a skewer, pierce a few holes into the cake's top. Pour the grapefruit/thyme syrup on the cake and allow it soak in. Let the cake cool to room temperature.
Pour the glaze over the cake and garnish with a few sprigs of thyme.