Cut carrots in half crosswise, then lengthwise into 1/2-inch-thick sticks. Put carrots and 2 tablespoons butter in an electric slow-cooker (4 1/2 qt. or larger) or a heavy 12-inch frying pan.
If using a slow-cooker, cover and set heat to high. Cook, stirring twice, until carrots are very tender when pierced, 2 to 3 hours. Drain. If using a heavy frying pan, set on a heat diffuser over a burner on low heat (see notes). Add 3 tablespoons water, cover with a round of cooking parchment and a tight-fitting lid, and follow cooking instructions for slow-cooker.
About 10 minutes before serving, melt remaining 2 tablespoons butter in an 11- to 12-inch frying pan over medium heat. Add garlic and parsley and stir until garlic softens, about 1 minute. Stir in carrots, olives, thyme, and salt and pepper to taste. Add cream, cover, and cook over medium-low heat until carrots are hot and cream is thickened and coats the carrots, 5 to 7 minutes. Pour into a serving dish.