Garlic custard with mushrooms and parsley sauce

This recipe from Provence is traditionally made with chanterelles, but any mushrooms will do. You need to be a real garlic lover to go to the trouble of making this one!

4 large bulbs (heads) of garlic
6 Tbsp extra-virgin olive oil
1 tsp sugar
Salt and freshly ground black pepper
3/4 cup full-cream milk
1/3 cup double cream
2 free-range eggs, lightly beaten
2 fresh Roma tomatoes, peeled, seeded, and coarsely chopped
4 cups coarsely chopped fresh parsley leaves and stems, plus additional sprigs for garnish
1 Tbsp butter
500g chanterelles or other mushrooms

Preheat oven to 180℃. Cut 3 heads garlic in half crosswise, place on a large sheet of aluminium foil, drizzle with about 1 tablespoon of oil, sprinkle with sugar, and season with salt and pepper. Tightly wrap foil around garlic and bake until soft, about one and a half  hours. Remove from oven, unwrap, allow to cool, then squeeze garlic pulp from cloves into a small bowl; discard skins.
Separate remaining head of garlic into cloves, peel, and slice each clove lengthwise as thinly as possible. Heat 2 tablespoons of oil in a small non-stick pan over medium-low heat. Add garlic slices and cook, stirring, until soft, about 5 minutes. Drain on paper towels.
Reduce oven to150℃. Place roasted garlic, milk, cream, and eggs in a food processor and purée until smooth. Lightly brush four ramekins about 7 cms wide and about 4 cms high, with 1 tablespoon of oil, then line the bottom of each with garlic slices. Spoon about 2 tablespoons of garlic custard into each ramekin, evenly divide tomatoes between ramekins, then cover with about 3 more tablespoons of custard.
Transfer ramekins to a roasting pan, place pan in oven, then add about 3 cms hot water to pan. Bake custards until set, about 30 minutes, remove from roasting pan, and allow to cool for about 20 minutes.
Meanwhile, blanch chopped parsley in a large pot of boiling salted water until bright green, 20–30 seconds. Drain, allow to cool, and transfer to a food processor. Add 1/4 cup water and purée until smooth. Squeeze juice through a clean muslin or Chux into a small pan. Discard parsley. Warm juice over low heat, then whisk in butter and set aside.
Heat remaining 2 tablespoons of oil in a medium pan over medium-high heat. Add mushrooms and cook, stirring until tender, 2–5 minutes, then adjust seasoning with salt and pepper. To serve, turn each custard out on to a medium plate and garnish with parsley sauce, mushrooms, and parsley sprigs.