Combine coconut oil, turmeric root, ginger root, and black pepper in a saucepan; add 1/2 of the water. Cook and stir mixture over medium until small bubbles form around the edges, 1 to 2 minutes. Reduce heat to medium-low; cook, stirring continually and adding small amounts of the remaining water, until mixture forms a paste, 5 to 8 minutes.

Transfer paste to a glass container and cool to room temperature. Cover container tightly with a lid and refrigerate.