Preheat oven to 375˚F. Butter a 6-cup soufflé dish or gratin dish and lightly dust with Parmesan cheese.

Stir together the garlic, cream, and thyme in a small saucepan over low heat. Bring to a boil, then turn off the heat, cover tightly, and allow to steep for 15 minutes.

Place the still wet spinach in a large hot skillet and wilt. Transfer to a colander and press out any moisture, then finely chop.

Melt 4 tablespoons of the butter in a saucepan. Stir in the flour and cook for 1 minute, stirring. Stir in the milk and whisk continuously until it thickens. Add 1 teaspoon of salt, the goat cheese, and Parmesan. Remove from heat, then stir in the egg yolks, chopped spinach, the garlic-thyme mixture, and a generous pinch of black pepper.

In a large bowl, whisk the egg whites and a pinch of salt until they form soft, slightly stiff peaks. Very gently fold the warm cheese and spinach mixture into the bowl of egg whites until incorporated. Scrape the batter into the prepared soufflé dish or gratin dish and bake until set and golden brown, roughly 30 minutes in a soufflé dish, or 25 minutes in a gratin dish.

Serve immediately.