For the grilled flatbread, first mix warm milk, water, sugar and yeast in a bowl and let stand for about 10 minutes.
Beat the eggs separately. Mix flour, salt and butter.
Combine yeast mixture and egg and mix with other dough ingredients. Knead dough well until silky smooth and let rest warm for an hour.
Lightly grease a cast-iron skillet and place on a hot grill.
Toss the tomatoes with the olives and chopped rosemary.
Press the mixture into the hot pan and press in the tomatoes and olives.
Unhook the pan from the grill (using a brick) and grill the flatbread indirectly, covered, for 25-30 minutes.
GRILLING METHOD: indirectGRILLING TIME: 25-30 minutes at approx. 180 °C