Of all soufflés, this is my favorite. The enticing aroma of goat cheese is very seductive, and the little pockets of melted cheese are like buried treasure. Although a classic soufflé dish forms a high, puffed crown, I often bake this and other soufflés in a large shallow gratin dish instead. It still looks marvelous, it bakes more quickly, and this way there's plenty of crust for everyone.
Preheat the oven to 400 degrees F. Butter a 6-cup soufflé dish or an 8-cup gratin dish and coat it with the Parmesan. Heat the milk with the aromatics until it boils. Set it aside to steep for 15 minutes, then strain.Meanwhile, cook the spinach leaves with water still clinging to them until tender. Strain. (You can use other greens as well; chard and tender kale come to mind.)
When the spinach is wilted, remove from pan and strain out the moisture and set aside. Melt the butter in a saucepan. When foamy, stir in the flour and cook over low heat for several minutes. Whisk in the milk all at once and stir vigorously for a minute or so as it thickens, then add 3/4 teaspoon salt, a few twists of pepper, and the cayenne. Remove from heat. Beat in the egg yolks one at a time until well blended, then stir in the cheese. Don't worry about getting it smooth. Finely chop the spinach and and season with salt, pepper, and a pinch of nutmeg. Add to the egg base. Season the mixture with salt and pepper.
Beat the egg whites with a pinch of salt until they form firm peaks, then stir a quarter of them into the base to lighten the mixture. Fold in the rest, transfer to the prepared dish, then put in the center of the oven and lower the heat to 375 degrees F. Bake for 30 minutes or until golden and just a bit wobbly in the center. Remove, scatter the thyme over the top, and serve immediately.