Preheat the oven to 180C/350F/Gas 4.
Place the flour, baking powder, butter and salt and freshly ground black pepper into a food processor and pulse until the mixture resembles breadcrumbs. Add the beaten egg and milk to bind the mixture, adding more flour or milk as necessary, then pulse again to form a dough. Add the torn spinach leaves to the food processor and pulse until roughly combined.
Knead the dough on a floured surface, then shape into a round and transfer onto a baking sheet. Using your fingertips, make six indentations, large enough to hold the cherry tomatoes in the top of the dough. Press the cherry tomatoes into the indentations, drizzle over the olive oil and bake in the oven for 10-12 minutes, or until golden-brown and cooked through.
Serve warm, in slices, with butter for spreading.