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Adjust oven rack to upper-middle position and heat oven to 450 degrees.
Whisk broth, honey, cornstarch, ¼ teaspoon salt, and cayenne together in small bowl; set aside.
Cut potatoes crosswise into 1-inch-thick rounds.
Toss potatoes with melted butter, pepper, and remaining 1 teaspoon salt in large bowl.
Arrange potatoes in single layer in 13 by 9-inch baking pan.
Roast until potatoes are tender when pierced with paring knife and bottoms are lightly browned, 30 to 35 minutes.
Remove pan from oven. Using flat metal spatula and tongs, loosen potatoes from bottom of pan and flip.
Add garlic to pan.
Whisk broth mixture to recombine, then pour around potatoes, avoiding tops of potatoes.
Continue to roast until liquid has reduced slightly, about 15 minutes longer.
Carefully transfer potatoes to serving platter, browned side up; discard garlic.
Stir sauce in pan to recombine, then spoon over potatoes.
Sprinkle potatoes with thyme. Serve.