Preheat the oven to 150°C.
Place halved tomatoes cut-side up on a roasting tray.
Season with thyme, salt, pepper, and olive oil.
Roast for 1 to 2 hours until moisture evaporates and tomatoes dry out.
Remove tomatoes and set aside to cool.
Blend pesto ingredients except oil and seasoning into a coarse purée.
Gradually incorporate oil until a thick purée forms and season to taste.
Preheat the oven to 200°C.
Heat olive oil in two 18-20cm ovenproof pans over medium heat.
Arrange sliced potatoes in overlapping circles on the pan bottoms.
Season and reduce heat to low.
Cook for 5 minutes until edges are golden and centers are translucent.
Spread rocket pesto over the potato layer.
Arrange sardines on top in a fan shape and sprinkle with oregano.
Bake in the oven for 15-20 minutes until the base is golden.
Cool slightly before removing the tarts from the pans.
Heat 2cm of vegetable oil in a frying pan until shimmering.
Fry capers until crispy then drain on kitchen paper.
Serve tart topped with roasted tomatoes, fried capers, and pecorino.