Transfer to a greased bowl, cover, and let it rise until nearly doubled, 1 to 1 1/2 hours. While the dough rises, make the filling.
To make the filling: Slice off the top of the garlic head to expose the cloves. Place cut side-down in a small microwave-safe bowl. Add the olive oil and water. Microwave, uncovered, for 4 to 6 minutes at 50% power, until the garlic cloves are soft. When cool enough to handle, squeeze out 4 to 6 garlic cloves (20g) into a medium bowl. (Save the rest of the garlic for another use or add more if you’re a garlic lover!)
Mash the cloves with a fork until smooth. Add the cream cheese, Parmesan, herbes de Provence, and salt; mix to combine.
To shape the tarte soleil: Divide the dough in half (335g per piece), shape each piece into a tight ball, cover, and let them rest for 10 minutes.
On a lightly floured surface, roll one ball into a 10 1/2" circle. Transfer to a sheet of parchment, then roll out the other ball to the same size.
Spread the filling over the dough on the parchment, leaving a bare 1/2" border. Brush the border with egg wash. Place the bare circle of dough on top of the filling; gently press to seal the borders together.
Gently place a 2 1/2" to 3" round cutter in the center of the dough and use a sharp knife or pizza wheel to cut the circle into 16 equal strips, from the cutter to the edge. It helps to work in quadrants: Cut the dough into 4 sections, then cut each section in half, then cut each of those sections in half again.
Remove the cutter from the center of the dough, and transfer the dough, parchment and all, to a baking sheet. Next, gently tug each strip away from the center, then twist 3 or 4 times in the same direction.
Cover the dough and let it rise for 45 to 60 minutes, until it's puffy and bounces back slowly when poked.
Near the end of the rising time, preheat the oven to 400°F with a rack in the center.
Brush the dough all over with egg wash. In a small bowl, mix together the Parmesan and the herbes de Provence, then sprinkle this mixture around the edge of the bread and in the center.
Bake the tarte soleil for 20 to 25 minutes, until deeply golden. Let cool slightly, then serve warm or at room temperature.
Storage information: Wrap any leftover tarte soleil airtight and store at room temperature for up to 2 days. To reheat, wrap the tarte soleil in foil and bake in a 325°F oven until warm, 10 to 15 minutes.
