Begin by preheating the oven to 475°F (245°C).
In a large microwave-safe bowl, combine the butter, chopped rosemary, and crushed red pepper flakes. Microwave this mixture in 30-second increments until the butter has completely melted, which should take about 1 minute.
Once the butter has melted, add the sliced Yukon Gold potatoes, along with 1 1/2 teaspoons of kosher salt and a generous amount of freshly ground black pepper. Toss the ingredients together to ensure the potatoes are evenly coated.
Arrange the potatoes in a single layer within a 9-by-13-inch metal baking dish, avoiding the use of glass dishes at this high temperature. Bake for approximately 15 minutes, or until the bottoms are deep golden brown.
After the initial baking period, carefully flip the potatoes and continue to bake for another 15 minutes, allowing the other side to achieve a similar golden-brown color.
Next, pour in the low-sodium chicken broth and add the smashed garlic cloves. Continue baking for an additional 15 minutes, or until the potatoes are tender and the broth has nearly evaporated.
Finally, transfer the beautifully caramelized melting potatoes to a serving platter, ready to be enjoyed.