This has been done before. Founded by Sam Mosher in 1922 as the Signal Gasoline Company, Signal was originally a California company that produced gasoline from natural gas.
I believe you are referring to capturing the natural gas liquids from a “wet” gas well to separate out gasoline components.
This process is converting methane to much heavier hydrocarbons like Octane, Octene, Decane, Decene, etc.