Many layered materials, such as graphene and transition metal dichalcogenides, can be exfoliated down to atomic or molecular monolayers. These materials exhibit exciting material properties that can be exploited for several promising device concepts. Thinner materials lead to an increased surface-to-volume ratio, with mono- and bi-layers being basically pure surfaces. Thin crystals containing more than two layers also often behave as an all-surface material, depending on the physical property of interest. As a result, flakes of layered materials are typically highly sensitive to their environment, which is undesirable for a broad range of studies and potential devices. Material systems based on suspended flakes overcome this issue, yet often require complex fabrication procedures. Here, we demonstrate the relatively straightforward fabrication of exfoliated MoSe flakes down to the monolayer, suspended over unprecedentedly large holes with a diameter of 15 µm. We describe our fabrication methods in detail, present characterization measurements of the fabricated structures, and, finally, exploit these suspended flakes for accurate optical absorption measurements.