Strip rosemary needles from stalks, chop finely. Dissolve yeast in nearly 10 oz. (300ml) water. Add flour, salt, olive oil and rosemary and knead until dough is smooth and elastic. Cover and leave to rise to twice the size.
Cut Gruyère into about 1/8" (3-5mm) thin slices. Halve cherry tomatoes. Pluck basil leaves from stalks.
Lightly dust sheet of baking paper with flour. Divide dough into two; roll out one half thinly into a rectangle on the baking paper and place with paper onto a baking tray. Spread dough with red pesto. Cover with ham and cheese. Distribute tomatoes with cut surface upwards. Sprinkle with basil.
Roll out remaining dough to same size, place on top of filling. Press edges together firmly. Brush surface with oil and prick several times with fork. Sprinkle with a little coarse salt.
Bake on bottom shelf of hot oven (425°F or 220°C) for about 15 minutes. Leave to rest for 10 minutes and cut into portions.