Rinse and scrub the potatoes lightly in a colander under running water. If the potatoes are on the smaller side–less than 1-inch wide and not very long–leave them intact. Slice any larger fingerling potatoes in half crosswise.
Place the fingerling potatoes in a straight-sided sauté pan (at least 3 quarts in size) so that the potatoes can be accommodated in a single layer. Add the sliced shallot, garlic cloves, fresh rosemary, thyme, and dried bay leaves to the pan. Add the olive oil and toss to coat evenly. Pour in the chicken stock and season lightly with salt and pepper (the salt will concentrate as the potatoes cook, so avoid over-seasoning, especially if you are not using low-sodium chicken stock).
Cover the pan and bring to a simmer over medium heat. Reduce the heat to a very low simmer and cook the potatoes, covered, for 10 minutes. Use a spoon to flip the potatoes, cover, and simmer for an additional 10 to 12 minutes, or until they are can be easily pierced with a sharp knife or skewer. There should still be a relatively substantial amount of braising liquid left in the pan.
Remove the lid and bring over high heat ntil the braising liquid has come to a boil. Continue to cook over high heat, shaking the pan back and forth gently, until all of the braising liquid has evaporated and the potatoes begin to sizzle in any remaining oil in the pan. At this point, the shallots and garlic will have reduced to a buttery glaze, which should coat the potatoes evenly. Remove from the heat, discard the bay leaves and any tough remaining rosemary and thyme stems. Taste and season with salt and pepper, if necessary.
Place the potatoes in a serving platter and garnish with chopped fresh thyme leaves. Serve immediately.