Preheat your oven to 325°F (165°C).
In a medium bowl, gently stir 1 tablespoon (15 ml / 0.5 fl oz) of the fresh thyme into the cooked beans.
Season generously with salt and pepper to taste.
Spread the seasoned beans in an even layer in a 9x13 inch (or similar size) baking dish.
Halve the peeled potatoes lengthwise, then use a sharp knife or mandoline to slice them thinly into half-circles (about 1/8-inch thick).
Arrange the potato slices in tight, overlapping rows over the bean layer, covering them completely.
Pour the vegetable stock evenly over the potatoes. Dot the top with the pieces of butter, then sprinkle with the remaining tablespoon of thyme, salt, and pepper.
Cover the baking dish tightly with aluminum foil and bake for 45 minutes.
Remove the foil and continue to bake for another 45-50 minutes, or until the liquid has reduced to a glaze and the potatoes are tender and beautifully browned on top.
Let the dish rest for at least 10 minutes before serving. It's delicious served hot or at room temperature.
Add a smoky depth by mixing 1 tablespoon (15 ml / 0.5 fl oz) of smoked Spanish paprika (pimentón) into the bean layer before topping with potatoes.
Sauté 2 cups (480 ml) of chopped leeks in butter until very soft (about 20 minutes) and spread them over the beans for an elegant layer of flavor.
While canned beans work in a pinch (rinse them well!) , using home-cooked beans provides a far superior texture and flavor that truly makes the dish shine.