Preheat the oven to 180 °C. Brush the vegetables clean, but do not peel them. Cut them lengthwise and lay them side by side, not on top of each other, on a baking sheet lined with parchment paper, pressing half of the fresh herbs: thyme, rosemary, oregano, and the unpeeled garlic cloves cut in half well between the vegetables. Then add the olive oil. Grill for 1 hour.
Prepare the emulsion: put the milk, water, bouillon cubes, thyme, and bay leaf in a large pot. Add coarsely chopped Parmesan and gently heat. Let it simmer on low heat for about an hour. Be sure to also add the rinds of the cheese, they are real flavor bombs.
Season the grouper fillets with pepper and salt on the colored side of the fish. Fold the grouper fillets into thirds, drizzle them with some olive oil. To get nice square packages, make 2 cuts in each fillet with a knife where you will fold them. Place them in the oven with the vegetables, and count on about 8 minutes of cooking time. Arrange the fish and vegetables nicely on the plates.
Before you blend the emulsion, first remove the bay leaf and thyme. Add the butter in cubes, and blend until you get a lightly frothy sauce. Blend just before plating and spoon some sauce over the grouper fillets and the grilled vegetables. Garnish with sprigs of thyme.