A non-dairy, vegetable based beverage is obtained from acorns by a process which is characterized in that it comprises the steps of:a) grinding a mixture of acorn nuts and water, optionally comprising enzymes to reduce the amount of starch,b) heating the ground mixture to provide starch swelling and subsequent cooling the heated mixture to a temperature below 65°C,c) optionally adding enzymes to the mixture of step b) to reduce the amount of starch in said mixture,d) fine grinding the watery mixture,d1) homogenizing the mixture.Preferably the process includes a step for removing tannins, wherein said tannin removal step preferably involves at least one of heating the mixture of ground acorn or applying vacuum to said mixture.