Bring a large pot of water to a boil and season generously with salt. Prepare a large bowl of ice water and set aside.
Drop large bunches of kale into the boiling water, working in batches, and stir gently until softened, about 3 minutes. Use a spider or large slotted spoon to transfer the kale to the ice bath.
Once cool, drain well, then use your hands to squeeze out as much liquid as possible. Coarsely chop and transfer to a large bowl.
Heat oil in a medium skillet over medium heat. Add breadcrumbs and stir until crisp and golden brown, about 5 minutes.
Transfer to a bowl, season lightly with salt and pepper, then stir in Parmesan cheese and 1 teaspoon thyme leaves.
Wipe out the skillet, then melt 1 tablespoon butter over medium-high heat.
Add shallots and cook until golden and crisp, about 7 to 8 minutes. Transfer to the bowl with kale.
In the same skillet, add the remaining tablespoon of butter and the flour.
Whisk until the flour is absorbed, then whisk in the half and half, garlic, and thyme sprigs. Bring to a simmer and cook until the mixture thickens and reduces to about 1 ½ cups.
Add nutmeg, then season with salt and pepper to taste (you can go a little heavier since it will be mixed with the kale). Discard the thyme sprigs and garlic cloves if desired, or leave the garlic in and mash it slightly with a fork.
Pour the sauce over the kale and toss to coat evenly. Taste and season again with salt and pepper.
Transfer to a greased 3-quart baking dish. Sprinkle with Gruyère cheese, then top with breadcrumbs. At this point, the dish can be prepared up to 3 days in advance. Cover and refrigerate until ready to bake.
Preheat the oven to 400°F. Bake, covered, for about 25 minutes, or until the filling is hot.
Remove the cover and continue baking until bubbling, golden, and melted, about 10 to 20 minutes more.
Sprinkle with the remaining thyme leaves and serve.