Prepare the vegetables by scrubbing the potatoes and cutting them into 1 1/2-inch chunks, coring and chopping the cabbage into large pieces, slicing the onion, and mincing the garlic.
Slice the kielbasa sausage into 1/2-inch thick rounds and set aside.
Add the potato chunks to the bottom of the slow cooker in an even layer.
Layer the sliced onion and chopped cabbage on top of the potatoes in the slow cooker.
Scatter the minced garlic evenly over the vegetables.
In a medium bowl, whisk together the low-sodium chicken broth, olive oil, Dijon mustard, apple cider vinegar, smoked paprika, dried thyme, kosher salt, and black pepper until well combined.
Pour the broth mixture evenly over the potatoes, cabbage, onion, and garlic in the slow cooker.
Arrange the sliced kielbasa sausage on top of the vegetables in an even layer.
Cover the slow cooker with the lid and cook on LOW for 6 to 7 hours, or on HIGH for 3 to 4 hours, until the potatoes are tender and the cabbage is soft.
Once cooked, gently stir the contents of the slow cooker to distribute the kielbasa, cabbage, and potatoes and coat everything in the cooking juices.
Taste and adjust seasoning with a little extra kosher salt or black pepper if desired.
Sprinkle the chopped fresh parsley over the top for serving, if using, and serve the slow cooker kielbasa with cabbage and potatoes hot, spooning some of the flavorful cooking liquid over each portion.