Granite Cobblestone is a block added by Better With Mods. Similar to vanilla Cobblestone, Granite Cobblestone is dropped when breaking Granite. The block was added for consistency with vanilla Minecraft's stone. Granite Cobblestone can be used in place of cobblestone in many recipes.
Granite Cobblestone, along with other Cobblestone drops from the mod, can be turned off in the config file under the HCCobblestone option.