Grease and/or line a muffin tin. In a large bowl, combine the flour, sugar and salt. Dissolve the yeast in a measuring cup filled with the warmed milk.
Combine the milk mixture, vegetable oil, vanilla extract, and egg into the flour mixture. Mix everything well, until it's very smooth. Pour a bit less than ¼ cup of the batter into each muffin cup in your prepared pan and let rest for 15 minutes.
While the batter rests, mix together the cubed, room temperature butter, brown sugar, cinnamon, nutmeg, and cloves in a small bowl using a fork or my preferred method, your hands, until all the butter has been incorporated into the sugar and mixture is crumbly.
Sprinkle the topping evenly onto the rested batter and press the mixture down into the dough with your fingertips. Place pan into a cold oven, then set the oven temperature to 350 degrees F. Bake for about 20 minutes, or until the cakes are lightly browned at the edges and the center springs back when lightly pressed. Some of the sugar mixture on top may still be bubbling.
Cool for at least 30 minutes before whisking the powdered sugar and milk together to form an icing and drizzling it onto the bread. Serve warm if you can, but they're great at room temperature or cold, too. Leftovers can be reheated in the microwave as well.