Preheat oven to 180°C (or 350°F). Line a muffin tray with muffin cases.
Drain the beetroot and add to a food processor. Add the yoghurt, sugar and vanilla. Process until smooth. You may need to scrape down the sides with a spatula as you go.
Add the flour, baking powder and egg replacement powder to a separate bowl. Whisk to combine.
Add the flour mix to the process. Process until just combined.
Spoon the mixture into the prepared muffin cases.
Bake for approximately 20 minutes, until browned on top and cooked through.