In a small bowl, dissolve the yeast in lukewarm water with a little sugar and let it foam (about 10 minutes).
In a large bowl, mix the flour with the remaining sugar and salt. Add the yeast mixture and olive oil. Knead into a soft and elastic dough. Cover it with a cloth and let it rise in a warm place for about 1.5 hours, until it has doubled in volume.
Seed and rinse the grapes. Divide the risen dough into two parts. Roll out the first part onto a baking sheet lined with parchment paper.
Spread half of the grapes evenly over the dough, sprinkle with half of the sugar, and cover with the second rolled-out piece of dough. Gently press the edges together.
Place the remaining grapes on top, pressing them slightly into the dough, sprinkle with the remaining sugar, and drizzle with olive oil. Preheat the oven to 190 °C (375 °F).
Bake for about 30 minutes, or until the surface is golden and crispy. Serve the Schiacciata warm, ideally cut into squares.