Presented here are the first kinetic two-dimensional Vlasov-Fokker-Planck calculations of inertial confinement fusion-related laser-plasma interactions, to include self-consistent magnetic fields, hydrodynamic plasma expansion and anisotropic electron pressure. An underdense plasma, reminiscent of the gas fill of a hohlraum, is heated by a laser speckle with I lambda(2) = 1.0 x 10(15) W cm(-2) mu m(2) and radius omega(0) = 5 mu m. Inverse bremsstrahlung absorption of the laser and non-local electron transport lead to the development of a collisional analogue of the Weibel electromagnetic instability. The instability is seeded by magnetic fields, generated in an initial period of linear growth due to the anisotropic electron distribution arising in a laser speckle. Using the circular polarization does not generate significant fields. For linear polarization, the field generally saturates when the magnetization is omega tau(ei) > 1, and the effective growth rate is similar to the coherence time of typical laser speckles. The presence of these magnetic fluctuations significantly affects the heat fluxes and hydrodynamics in the plasma.