For the dough, combine the water, yeast, sugar and olive oil and let stand for 5 minutes until foamy. In a large bowl, mix together both flours and the salt. Add the wet ingredients to the dry and stir until it forms a shaggy dough. Turn the dough onto a lightly floured work surface and knead for 10 minutes until the dough is smooth and elastic. (Alternatively, the dough can be mixed in the bowl of a stand mixer using a dough hook.)
Gather the dough into a ball, transfer to an oiled bowl and cover. Place the bowl in a warm spot to allow the dough to rise until it has doubled in size, about 1-1/2 – 2 hours.
For the jam, combine the cranberries, figs, sugar, lemon peel and water in a large saucepan. Bring the mixture to a boil over medium high heat, stirring frequently. Reduce the heat and simmer the jam until thickened, about 20 minutes. Let the jam cool to room temperature. Discard the lemon peels.
Preheat the countertop oven to 400 degrees F.
On a lightly floured work surface, divide the dough into 12 balls. Roll each ball into a 6-inch by 3-inch rectangle. Spread with brie and cranberry jam leaving a 1/4-inch border. Starting with a long side, roll the dough into a log. Use a knife to slice it in half lengthwise, leaving a half-inch uncut at one end. Twist the ropes together, tucking the edges underneath and pinching them together.
Bake the rolls on a parchment-lined sheet pan for 12-15 minutes until golden brown. Sprinkle with chopped fresh rosemary and flaky sea salt before serving the rolls warm.