A process for producing golf ball including a core and a cover layer, wherein the cover layer provides one or more deep dimples that extend through the cover layer and/or into a layer or component underneath is disclosed. The cover may be a single layer or it may include multiple layers. If the cover is a multi-layer cover, the dimples extend to or into at least the first inner cover layer, and may extend into two or more inner cover layers. If the cover is a single layer, the dimples extend into the core. The dimples may be spherical or non-spherical, and the portion of the dimple that extends to or into the next inner layer may be the same or different shape as the outer portion of the dimple.