Adjust oven rack to middle position. Place 2 large sheets of heavy-duty aluminum foil on a work surface. Working with 1 sheet at a time, place half of potatoes in center along with 3 sprigs of thyme. Fold up foil and crimp edges to seal tightly. Repeat with other half of potatoes and 3 sprigs of thyme. Transfer pouches to a rimmed baking sheet and place in oven. Set oven to 300°F (150°C). Roast until a thin skewer inserted into potatoes meets some resistance, 1 hour 30 minutes to 1 hour 45 minutes.

Carefully unwrap and discard foil and thyme sprigs and place unwrapped potatoes in even layer on same sheet pan. Increase oven temperature to 400°F (205ºC), and roast until sweet potatoes are caramelized and a thin skewer inserted into potatoes meets no resistance, about 30 minutes.

Remove potatoes from oven and set aside until cool enough to handle, about 20 minutes.

While sweet potatoes are cooling, melt butter in a medium saucepan over medium-low heat, swirling gently, until particles are pale golden brown and smell nutty, about 10 minutes. Immediately transfer to a large bowl or the bowl of a stand mixer fitted with a whisk attachment. Add maple syrup. Pick leaves off of remaining 2 thyme sprigs, roughly chop (¼ teaspoon), and add to bowl with butter and maple syrup.

Peel sweet potatoes and discard skins and any juices. Add flesh to bowl with butter mixture. Beat with whisk attachment or a handheld mixer on medium-low speed until smooth and fluffy, about 2 minutes. Season to taste with salt. Serve.