Boil the potatoes in salted water until just tender, drain and allow to cool a little. Put the flour and yeast into a large bowl. When the potatoes are cool enough to handle, coarsely grate half straight into the mix, tossing occasionally to coat in the flour. This will stop the potatoes sticking in clumps.
Grate in half the courgette, add half of the cheese and strip in half of the thyme leaves. Add 1 tbsp olive oil mixed with 175-200ml hand-warm water. Bring the dough together and knead for a couple of mins. Put into a lightly oiled bowl, cover and leave to rise in a warm place until doubled in size.
Heat oven to 200C/180C fan/gas 6. Grease a 20cm x 30cm tin. Push the bread dough into the tin firmly, pushing out air. Finely slice the remaining potatoes and courgette. Scatter over the top along with the remaining thyme and poke in roughly with your fingers so the slices stick out a little. Cover with oiled cling film and leave to rise again for about 45 mins. Drizzle with the rest of the olive oil, scatter with the remaining cheese, then cook for 50 mins-1 hr, until well risen and golden. Leave to cool, then serve, cut into squares.