Mix the flour, yeast, salt, water and olive oil in a bowl to form a sticky dough, then turn out onto a floured work surface and knead until smooth and silky. The dough should also “bounce back” when you poke it. If you have a food mixer with a dough hook, you could use this instead, but keep an eye on the dough as it won’t need 10 minutes in the mixer.
Shape the dough into a ball and place in a lightly oiled bowl. Cover with a plastic bag or cling film and leave in a warm place until it doubles in size (this should take about an hour). Once the dough has risen, turn it onto a clean surface and press it into a rough rectangle. Transfer to an oiled 8x12-inch roasting tray and cover with a plastic bag. Leave it to rise for another hour, until it’s doubled in size again and airy.
Preheat the oven to 490° F (250° C), or as high as it will go. Push straight down with your fingers all over the dough to form holes almost to the bottom of the tray. Push the tomato halves and rosemary sprigs into the holes and drizzle over more olive oil and sprinkle a generous pinch of sea salt.
Place the focaccia in the centre of the hot oven for 10 minutes, then turn the heat down to 400° F (200° C) and cook for a further ten minutes. Take the focaccia out of the oven and drizzle more olive oil over. Allow it to cool for 10 minutes before slicing into squares in the tin.