Gas cock for gas burner, preferably a professional gas burner provided with a pilot flame, comprising: - a cock body wherein a plug receiving seat and a gas passage opening for the passage of the gas from or to the plug receiving seat are formed, and - a conical plug, comprising a side wall which extends around a central conical plug axis and which is housed gas-tight in the plug receiving seat, said side wall comprising an inner wall surface which defines an inner cavity of the conical plug and an outer wall surface opposite to the inner wall surface, said conical plug comprising a plug opening for the passage of gas from or to the plug receiving seat through the inner cavity of the conical plug according to an adjustable angle of rotation (α) between the cock body and the conical plug, wherein in the side wall of the conical plug, a groove is formed on the side of the outer wall surface, said groove being connected to the plug opening, wherein said groove is adapted to be positioned at least partially at the gas passage opening of the cock body as a function of the adjustable angle of rotation (α), wherein said groove comprises at least one modulating portion which extends predominantly between a first angular position and a second angular position along a circumferential direction of rotation of the conical plug, wherein said groove, between the first angular position and the second angular position has an increasing or decreasing depth, said depth being measured in the radial direction perpendicular to the side wall, said gas cock being characterized in that downstream of the second angular position, in the direction that proceeds from greater depth to smaller depth of the groove, a blind pocket is obtained, having a pocket depth greater than the depth of the groove measured at the second angular position. - a cock body wherein a plug receiving seat and a gas passage opening for the passage of the gas from or to the plug receiving seat are formed, and - a conical plug, comprising a side wall which extends around a central conical plug axis and which is housed gas-tight in the plug receiving seat, said side wall comprising an inner wall surface which defines an inner cavity of the conical plug and an outer wall surface opposite to the inner wall surface, said conical plug comprising a plug opening for the passage of gas from or to the plug receiving seat through the inner cavity of the conical plug according to an adjustable angle of rotation (α) between the cock body and the conical plug, wherein in the side wall of the conical plug, a groove is formed on the side of the outer wall surface, said groove being connected to the plug opening, wherein said groove is adapted to be positioned at least partially at the gas passage opening of the cock body as a function of the adjustable angle of rotation (α), wherein said groove comprises at least one modulating portion which extends predominantly between a first angular position and a second angular position along a circumferential direction of rotation of the conical plug, wherein said groove, between the first angular position and the second angular position has an increasing or decreasing depth, said depth being measured in the radial direction perpendicular to the side wall, said gas cock being characterized in that downstream of the second angular position, in the direction that proceeds from greater depth to smaller depth of the groove, a blind pocket is obtained, having a pocket depth greater than the depth of the groove measured at the second angular position.