Place dried split peas, ham, potatoes, carrots, and garlic in the bottom of the slow cooker. Pour in chicken broth. Stir in bay leaf and parsley. Cook on low for 8 to 10 hours (or on high for 4 to 5 hours). Taste and add salt and pepper as needed.
You can dice your carrots if you prefer more noticeable bites of carrot, but I like shredding mine because they practically melt into the soup and my kids don't spend time trying to avoid them.
The amount of liquid in this recipe should be more than sufficient, but any time you cook a dried bean recipe in the crock pot for the first time, you'll want to check your water/broth level every once in awhile to make sure too much hasn't been soaked up by your beans/peas. If it has, just add more water/broth and stir. Some crock pots run hotter than others.
I use 8 cups of water and add a big tablespoon of Better Than Bouillon chicken base in lieu of chicken broth. Just be aware that BTB is pretty salty, so start with a conservative amount and add more if needed. I usually don't end up adding salt at the end when I use BTB.