In a large bowl, beat the whole eggs and yolks with the brown sugar, brown rice syrup, honey and fine sea salt. Gradually whisk in the rosemary butter, then whisk in the cream, flour and vanilla. Pour the filling into the tart shell and sprinkle flaky sea salt on top. Bake the tart for 50 minutes, until the filling is set at the edge but slightly jiggly in the center. Let cool completely. Serve at room temperature or slightly chilled, topped with a dollop of whipped crème fraîche alongside.