We present Atacama Large Millimeter Array (ALMA) Band 6 observations at 14−20 au spatial resolution of the disk and CO(2-1) outflow around the Class I protostar DG Tau B in Taurus. The disk is very large, both in dust continuum (R_{eff, 95%} = 174 au) and CO (R_CO = 700 au). It shows Keplerian rotation around a 1.1 ± 0.2 M_⊙ central star and two dust emission bumps at r = 62 and 135 au. These results confirm that large structured disks can form at an early stage where residual infall is still ongoing. The redshifted CO outflow at high velocity shows a striking hollow cone morphology out to 3000 au with a shear-like velocity structure within the cone walls. These walls coincide with the scattered light cavity, and they appear to be rooted within < 60 au in the disk. We confirm their global average rotation in the same sense as the disk, with a specific angular momentum ≃65 au km s⁻¹. The mass-flux rate of 1.7−2.9 × 10⁻⁷ M_⊙ yr⁻¹ is 35 ± 10 times that in the atomic jet. We also detect a wider and slower outflow component surrounding this inner conical flow, which also rotates in the same direction as the disk. Our ALMA observations therefore demonstrate that the inner cone walls, and the associated scattered light cavity, do not trace the interface with infalling material, which is shown to be confined to much wider angles (> 70°). The properties of the conical walls are suggestive of the interaction between an episodic inner jet or wind with an outer disk wind, or of a massive disk wind originating from 2 to 5 au. However, further modeling is required to establish their origin. In either case, such massive outflow may significantly affect the disk structure and evolution.