Mix the flour, olive oil, butter, salt, and baking powder in the food processor at high speed until you get 'bread crumbs'.
Add the egg and six tablespoons of cold water and mix until a cohesive dough forms. Wrap in plastic wrap and let rest in the refrigerator for at least one hour.
Preheat the oven to 200 °C. Roll out the dough and place it on a flat baking sheet lined with baking paper.
Cut out circles from the dough and place them in separate baking molds with the edges slightly raised. Prick the bottom and stay one centimeter from the edge.
Spread the tapenade in the center of the dough. Halve the cherry tomatoes and distribute them (cut side up) along with the goat cheese over the tart bases.
Sprinkle with oregano, some pepper, and salt. Drizzle with olive oil.
Brush the edge with the beaten egg yolk.
Bake the molds in the oven for ten to twenty minutes.
Just before serving, sprinkle the basil over the top.