large Yukon Gold potatoes (each about 6 ounces and 3 inches long) • high-heat cooking oil (such avocado or canola) • Salt and pepper • salted butter, diced • thyme or 2 rosemary sprigs, plus 1 sprig for garnishing • large garlic cloves, smashed and peeled • chicken broth (not low-sodium) or vegetable broth • Flaky salt (optional), for serving