Place one rack in the middle of the oven and one in the upper third. Heat to 425°F. Bring a large pot of salted water to a boil.
Cut one of the heads of cauliflower into bite-size florets. Transfer to a sheet pan along with the garlic cloves. Drizzle with 2 tablespoons of the oil and season with 1 teaspoon salt and several grinds black pepper; toss to coat. Roast until tender, 20 to 25 minutes.
Slice the remaining head of cauliflower into florets. Add to the boiling water along with the thyme sprigs. Cook until very tender (a knife should easily slide through), 8 to 10 minutes. Don't drain the water!
Meanwhile, combine the panko, 1/2 cup of the Parmesan, the remaining 1 tablespoon olive oil, and a pinch each salt and black pepper in a medium bowl. Set aside.
When the boiled cauliflower is tender, use a slotted spoon to transfer the florets to a food processor or high-speed blender. Return the water to a boil. Add the pasta and cook according to package directions for al dente. Reserve 1 cup of pasta water and drain.
When cool enough to handle, squeeze the roasted garlic out of their peels and add to the food processor/blender. Add the cottage cheese, milk, Dijon, cayenne, and several grinds black pepper. Process until very smooth, about 1 minute.
Add 1 1/2 cups of the Gruyere and the remaining 1/2 cup Parmesan and process again until smooth. Taste and season with salt, as needed (the amount you need will depend on the size of your cauliflower, the saltiness of your cottage cheese, etc. Remember you’ll also be adding some salty pasta water in a minute).
Return the pasta and the roasted cauliflower to the pot, add the sauce, and toss, adding a few splashes of pasta water until the sauce evenly coats the pasta. Taste and season again with more salt as needed. Heat the broiler.
Transfer the mixture to the now-empty sheet pan and spread into an even layer. Top with the remaining 1/2 cup Gruyere, followed by the bread crumb mixture. Broil until the bread crumbs are golden brown, 3 to 5 minutes. Garnish with fresh thyme leaves.
