Heat olive oil in a large skillet over medium-high heat; saute garlic until fragrant, about 1 minute. Add kale to garlic, working in batches if needed; cook and stir until beginning to wilt, about 5 minutes.
Stir water and vegetable base together in a small bowl until dissolved; pour over kale. Cook mixture until liquid is reduced, 1 to 2 minutes. Mix soy sauce and black pepper into kale.