We suggest a novel source of polarization-entangled photon pairs based on a cross-shaped plasmonic nanoantenna driven by a single quantum dot. The integration of the nanoantenna with a metal mirror overcomes the fundamental tradeoff between the spontaneous emission (SE) enhancement and the extraction efficiency typical of microcavity and nanowire-based architectures. With a very-high extraction efficiency of entangled photons (~90%) at 1.55 um and large SE enhancement (~90) over a broad 330 nm spectral range, the proposed design will pave the way toward reliable integrated sources of nonclassical light.