Arrange baby potatoes in a 10-inch nonstick skillet so they fit snugly with a little space between them.
Add rosemary, thyme, chicken broth, olive oil, 1 tablespoon butter, and kosher salt.
Heat skillet on high and bring to a boil. Reduce heat to medium, add garlic, and partially cover the skillet, leaving a small opening.
Simmer for 20 minutes, keeping the liquid gently boiling, until potatoes are fork-tender.
Add additional ½ cup broth or water if liquid has fully absorbed; liquid should cover about one-third of the potatoes.
Remove skillet from heat and gently press potatoes with a meat mallet or spoon until skins crack.
Return skillet to high heat, uncovered, and cook until liquid evaporates and bottoms are golden brown, about 12 minutes.
Remove from heat, flip potatoes, scrape up browned bits, and add remaining tablespoon of butter.
Press potatoes again lightly if needed and cook until second side is browned, about 5 minutes.
Sprinkle with parsley, season with salt, and serve warm.