Pulse flour, butter, sugar, and egg in a food processor until it forms a dough.
Wrap the dough ball in cling film and chill in the fridge for at least one hour.
Roll out the pastry on a floured surface, press into a 20cm tart case, and chill for 45 minutes.
Preheat the oven to 180°C.
Bake the chilled tart case for 10 to 15 minutes until golden-brown, then allow to cool.
Lower the oven temperature to 180°C.
Heat butter and oil in a large saucepan over low heat.
Gently cook onions and garlic with seasoning for 30 to 40 minutes until very soft.
Whisk eggs, egg yolks, mustard, and cream together in a bowl.
Mix onions into the egg mixture, spoon into the tart case, and bake for 20 to 25 minutes.
Combine all beans and chopped mint in a large bowl.
Whisk Dijon mustard, lemon juice, vinegar, seasoning, and olive oil to make the dressing.
Mix the dressing into the bean salad.
Serve warm tart wedges with a spoonful of bean salad.