Combine salt, pepper, rosemary, and thyme in a small bowl.
Remove and empty the hot jars from the canner and turn the canner on again to bring the water to a low simmer (180°F).
Distribute spices evenly among jars (1 ¼ teaspoon in pints, 2 ½ teaspoon in quarts).
Fill each jar with peeled and chopped potatoes to 1-inch headspace.
Add boiling broth to each jar to 1” headspace; use a tool to release any bubbles, then add more hot broth if needed.