Preheat the oven to 350°F. Line a muffin pan with 4 paper liners and set aside.
In a medium bowl, mix together the oil, sugar and vanilla extract until fully combined.
Whisk in the egg white and Greek yogurt until just combined.
Sprinkle the flour, baking powder and salt evenly over the batter and stir until just combined.
Divide evenly in the prepared muffin pan and bake in the preheated oven for 17-20 minutes, or until a toothpick inserted comes out clean. Allow cupcakes to cool.
Frosting: Beat the butter in a small bowl with an electric mixer until light and fluffy. Add in the powdered sugar, 1 Tbsp heavy cream and vanilla. Beat until light and fluffy, adding more cream if necessary.
Scrape the frosting into a piping bag with your choice of piping tip. Pipe the frosting onto the cooled cupcakes.