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Unroll the pastry and cut out a circle 1cm (½ in) larger in diameter than the rim of your frying pan. Transfer pastry to a baking sheet and chill until needed. Preheat oven to 190°C (170°C convection) or 375F.
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Peel and cut onions into equal size wedges through the root (this will help keep layers together).
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Melt butter, oil and sugar in the frying pan. Remove pan from heat and arrange onions in concentric circles, with a cut side down. Return pan to medium heat and cook for 10-12min until onions begin to caramelise on the underside (try not to disturb wedges or they’ll lose their shape).
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Add thyme, port, petimezi, garlic, and generous salt. Cook and let the onions bubble for 3 to 5 minutes, until pan juices start to thicken, then remove from heat and cool for 10min.
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Carefully cover onions with the pastry circle, tucking pastry down into the sides. Make a few small slits in the pastry with a sharp knife to allow steam to escape.
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Put pan into the oven for 20-25 min or until pastry is puffed and golden.
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While the tart is baking, whip together all the ingredients for the feta-mastiha cream in a food processor and set aside in the fridge to firm up.
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Remove the tart and let it rest at room temperature for 5 minutes, then carefully invert on to a board or plate. Garnish with more thyme, if you like, and serve hot or at room temperature, garnished with a dollop of the mastiha-feta cream.