Slice ends off of potatoes and peel. Cut each potato crosswise into ~2-inch cylinders.
Heat avocado oil in a large cast iron skillet (or other oven safe skillet) over medium heat until hot and shimmering. Add potatoes in a single layer, leaving a little room between each one and season with salt and pepper. Let cook until golden brown on one side, 5-6 minutes (check at 4 minutes and reduce heat if potatoes are browning too quickly). With tongs, flip each potato, season with salt and pepper and cook until golden brown on the other side, 5-6 minutes more. Scatter butter pieces around potatoes and gently swirl pan to distribute as it melts and foams. Add chicken broth and sprigs of rosemary and thyme along with smashed garlic cloves to pan; bring to boil. Spoon broth mixture over potatoes.
Transfer skillet to preheated oven and bake until tender, 30 to 35 minutes. Serve hot in skillet or transfer to serving platter. Spoon pan sauce over potatoes and garnish with fresh thyme leaves if desired.
Serve the tender, roasted garlic cloves along with the potatoes or eat them yourself - cook's treat!