Quarter the figs. Using a saucepan, heat the butter, apple syrup and balsamic vinegar until it bubbles. Turn down the heat to low. Arrange the quartered figs cut side down and cook for about 30 seconds. Allow them to cool in the sauce, turning over periodically. Peel a 2 cm chunk of fresh ginger and use a garlic press to mince. Prepare the dressing by whisking together the ginger, walnut oil, lemon juice, 1 tbsp of juice from the stewed figs and the neutral oil. Break or slice (using a Parmesan knife) the Beemster XO into pieces.
Toss the baby leaf salad greens with 3 tbsp of walnut-ginger dressing and divide the salad among 6 plates. Divide the figs and chunks of cheese among the plates and toss lightly with the greens. Drizzle a little more dressing and stewed fig juice around the salads