Pull the kale off the stems and coarsely chop the leaves. Toss them in a pot of boiling water (even an inch or two will allow the kale to steam), cover and cook for 4-5 minutes. Drain well.
In a large, heavy skillet heat a drizzle of oil and a blob of butter over medium-high heat. Add the kale and garlic, sprinkle with salt and pepper and cook, stirring occasionally, for a few minutes, until the moisture has cooked off. Set aside in a bowl.
Thinly slice the potatoes crosswise as thin as you can. Brush the bottom of the pan with oil or melted butter and layer in one third of the potato slices, overlapping slightly. Dab potatoes with some of the butter.
Spread half of kale over the potatoes, then another third of the potatoes, the remaining kale and the remaining potatoes.
Rub a sheet of foil with soft butter or brush it with oil, and place it buttered side down on top of the potatoes. Place a 10-inch heavy skillet on top of foil to weigh the galette down.
Cook over medium-how heat until the underside is golden brown, 10-12 minutes. Remove top skillet and foil. Set a dinner plate (as big as the pan) onto the top (a cookie sheet works fine too, but is a little more awkward to handle) and invert the galette. Slide it back into the skillet, browned side up, and cook, uncovered, until underside is golden brown and potatoes are tender, 12 to 15 minutes. Slide onto a serving plate. If any of it comes apart at any point, don't worry - just stick it back together.
Cut into wedges to serve.