Ultra-cold atomic gases realize clean and controllable model systems for investigating many-body quantum physics. In particular, a strongly interacting Fermi gas offers an excellent testbed for beyond-BCS superconductivity theories. One of the problems which complicates the interpretation of these experiments is the inherent density inhomogeneity of the gas which arises due to the harmonic confinement. Here we present a new technique to overcome this difficulty by spatially selecting only part of the cloud for interrogation. This selection is done by optical pumping atoms to a dark state using a beam with a high order Laguerre-Gaussian mode. We present measurements of the momentum distribution of a degenerate gas of ⁴⁰K atoms showing a convergence to a homogeneous-like behavior as we selectively probe more from the center of the cloud.