Heat the olive oil in a large skillet over medium heat.
Add the baby potatoes and sprinkle with ½ teaspoon kosher salt. Cook for about 5 minutes until the potatoes begin to brown.
Pour in the water, cover the skillet, and reduce the heat to medium-low. Cook for 5–10 minutes until the potatoes are fork tender. Remove the potatoes from the skillet and set aside in a bowl, loosely covered with foil.
Add the vegan butter to the same skillet and increase the heat to medium.
Once the butter melts, add the chicken pieces, minced garlic, and Italian seasoning. Sprinkle the remaining salt and black pepper over the chicken.
Cook for about 7 minutes, stirring occasionally, until the chicken is fully cooked with no pink remaining.
Return the potatoes to the skillet and gently stir everything together. Cook for another 1–2 minutes until warmed through.
Stir in the fresh parsley and remove from heat.
Serve the Garlic Butter Chicken and Potato Skillet immediately while hot.