In the bowl of an electric mixer fitted with the paddle attachment, stir together the water, milk, cane sugar and yeast. Let the mixture sit until foamy, about 10 minutes. Add the flour, olive oil and fine sea salt to the yeast mixture and mix well on low. Attach the dough hook, raise the speed to medium low and knead the dough for 8 minutes more.
Brush a large bowl with olive oil. Scrape the dough into the bowl and brush the top with additional oil. Cover with plastic wrap and let it rise in a warm place until it doubles in bulk, about 1 1/2 hours.
Gently press the dough down and then turn it out onto a floured surface and divide it into 2 balls. Brush a large baking sheet (or 2 smaller baking sheets) with olive oil, place the balls of dough on it and brush the tops with more oil. Set aside for 20 minutes, lightly covered with a kitchen towel.
After 20 minutes, dip your fingers in olive oil and press and stretch each ball of dough into an 8- to 9-inch circle. The dough will be dimpled from your fingers. Cover again with the towel and let rise for another 1 1/4 hours in a slightly warm place.
Preheat the oven to 450 degrees F.
Brush the tops of the dough with olive oil and sprinkle the grapes, raw sugar, coarse sea salt and rosemary evenly over the dough. Bake until the crust is golden brown and puffed around the edges, about 15 minutes. Let cool a bit before serving. Serve warm or at room temperature.