Pre-heat your oven to 390°F (200°C/180°C fan forced).
Grease and line your cake tin.
Zest the lime for the cake, then juice it.
Cut he feijoa in half and scoop out the flesh. You will need about one and a half cups of feijoa flesh or about 300 gms. Roughly mash the feijoa flesh with a fork.
Cut the butter and put it in a bowl with the sugar. Mix with an electric hand held beaters or in a stand mixer until creamed and pale looking.
Add the eggs one at a time and mix well between each addition. Add the lime zest, lime juice and vanilla and mix well.
Add the feijoa flesh and mix until just combined. The batter may start to look a little curdled at this point. This is normal and it will come together when you add the flour.
Add the flour and mux until just combined. Tip into the lined cake tin, smooth it down and bake the cake for 45 - 50 minutes or until golden brown.
Allow to cool completely before decorating.