Heat the onion and the carrots in the olive oil in a large pot over medium heat for about five minutes.
Add the chicken breast, potatoes, chicken seasoning, water, and broth. Bring to a boil, then reduce heat to a simmer.
Cook until chicken is cooked through and potatoes are tender, about 30 minutes. Use a spoon to remove any foam that rises to the top.
In a small cup, whisk together the cornstarch and non-dairy milk. Drizzle the mixture slowly into the pot, stirring constantly until the broth thickens.
Add the dried dill and pepper, stir.
Let cook for a few more minutes so the flavors combine.