Preheat oven to 350 degrees. Using a fork, poke several holes in the potatoes and microwave them for about five minutes until they are soft. Using a fork and knife, cut up the potatoes in the bowl and set aside.
In a cake tin or round baking dish (9-inch recommended), wipe the inside with olive oil. Arrange the puff pastry sheet inside, so that the edges hang over the bowl. Drizzle the potatoes with a bit of olive oil, toss, and arrange in the bottom of the puff pastry.
Crack three eggs in the potato bowl, and whisk them until they are thoroughly beaten. Add the cream, and a pinch of salt and pepper, and mix together. Then mix the cheese in as well. Pour the mixture over the potatoes.
In the same potato bowl again, mix the tomato sauce, tomato paste, and all remaining seasonings (grated garlic, basil leaves, herbs, cumin, crushed red pepper, harissa, smoked paprika). Also add in your 'fixings' at this time if you'd like to include them.
Carefully pour the tomato mixture over the top of the quiche. Do not stir. Sprinkle with sea salt and black pepper.
Using your fingers or a paper towel, carefully brush the exposed puff pastry with olive oil, so it doesn't burn. Bake in the oven at 350 degrees for about 35-40 minutes, on a lower oven rack. Check after 15 minutes, if the exposed pastry dough is burning, turn the oven heat down about 35-50 degrees.
Once ready, remove from the oven, make three indentations and crack the eggs into the top of the dish* Return to the oven until your eggs are done to your liking. Chill and allow to set before reheating in the oven to serve. *PLEASE NOTE: If you are making this the night before, remove from the oven and chill before cracking the last three eggs on the top. You can do that after chilling and setting, when you reheat it in the oven to serve. They will be fresher that way.