Bring a medium pot of water to a boil. Add the carrots and cook until slightly softened, but still crisp. Don't overcook them unless you like your pickles soft. Remove carrots from boiling water and immerse them in ice water to cool.
Layer dill sprigs, garlic and carrots in a glass food storage container or jar.
Mix 3 cups of water, vinegar, salt, dill seeds and peppercorns in the same medium saucepan that you cooked the carrots in. Bring to a boil to dissolve the salt. Pour brine over dill, garlic, and carrots. Let the jar sit at room temperature until cool, then cover and refrigerate to chill completely. Will last in the fridge for about 1 month.