Bring the vinegar, 3/4 cup water, salt, and brown sugar to a boil in a medium stainless steel saucepan. Stir, dissolving the salt and sugar.
Heat a 1-quart jar: Fill it with hot water and let it sit a couple minutes before pouring out. (The heat will prevent shattering when you pour in the boiling brine.) Add garlic, hot pepper, and spices.
Pack the jars tightly with carrots. Pour in hot brine. Cover and let cool overnight before eating.
Tasty Tip: These zesty slices are a great snack straight from the jar, but they're also amazing in fish tacos, layered on sandwiches, or tossed in salads
Spiced carrots can be stored in the refrigerator for up to three weeks.