Preheat your oven to 400°F. Slice your russet potatoes into 2-inch large cylinders lengthwise, you can leave the skins on. With a cylinder or cake mold, press down to make your large circles (about 1 1/2 to 2 inches wide). Season with kosher salt. (Use the unused parts of the potatoes for potato skin chips, mashed potatoes, hash browns, or potato soup!) Makes about 13 to 15 potatoes. (I like to use the mold here to get even circles, but you can also peel the skin, and cut around to make your circular potatoes).
In a large ovenproof cast iron skillet, stainless steel pan, or skillet, melt your neutral oil until glistening on medium-high heat. Add your potato rounds to the skillet, arranged flat and all in an even layer. Char and saute your potatoes, until they turn golden brown on their bottoms, about 7 to 8 minutes on each side, then flip and repeat.
When you flip your potatoes to the other side, add in your garlic, flesh side down, with the skins up, and your fresh rosemary.
Next, add in your butter to melt throughout, then add in your broth and sprinkle with kosher salt and black pepper.
Baste consistently to ensure you are topping a good amount of broth and butter over the tops of your potatoes.
Transfer to the oven to roast for 30 to 40 minutes, until the potatoes are fork tender, and the garlic is soft. Baste more broth halfway through cooking in the oven.
Remove from the oven, and use tongs to squeeze your roasted garlic out of its skin. Plate your potatoes, and top with any remaining broth/sauce poured over with the garlic.