To toast the breadcrumbs:
Melt the butter in a skillet over medium heat.
Add the garlic, breadcrumbs, thyme, and salt.
Cook, stirring often, until nicely toasted, about 3 to 5 minutes.
Transfer to a small bowl and set aside.
To cook the kale and portobello:
Wipe the skillet clean and melt 1 tablespoon of the butter over medium heat.
Add the garlic and kale, still wet from washing. Season with salt and pepper.
Cover the pan and let the kale steam until wilted and soft, about 5 minutes, lifting the lid and turning the kale a couple of times while it cooks.
Transfer the cooked kale to a plate and set aside.
Wipe the skillet again and melt the remaining tablespoon of butter over medium heat.
Add the sliced portobello and sauté until softened and just starting to turn golden brown, about 5 minutes.
To assemble and bake:
Heat the oven to 350°F and arrange a rack in the middle.
Coat 2 small oven dishes (8-ounce gratin dishes are ideal) with butter.
Divide the cooked kale among the dishes. Distribute the portobello slices on top of the kale.
Crack 2 eggs into each dish and crumble the cheese on top.
Dribble 1 tablespoon of heavy cream over each dish and sprinkle with 2 or 3 tablespoons of the toasted breadcrumbs.
Bake the eggs until set, about 10 to 12 minutes. Serve immediately.