Edible air-in-oil systems, also referred to as oleofoams, constitute a novel promising material for healthier, low-calorie fat replacers in confectionary products. Oleofoams can be formed by whipping oleogels, which are dispersions of fat crystals in an oil phase. Understanding how the properties of the fat crystals (i.e., size, shape, and polymorphism) contained in oleogels affect the microstructure and stability of oleofoams is essential for both the efficient design and manufacture of novel food products. In this work, cocoa butter, one of the main fat phases present in confectionary productions, which is responsible for pleasant texture and mouthfeel properties, was mixed with high oleic sunflower oil and crystallized to obtain an oleogel. This was subsequently whipped to yield a stable, highly aerated oleofoam. The effect of the crystallization conditions (oleogel composition and cooling rate) on the properties of the oleogels and related oleofoams was investigated with a multitechnique characterization approach, featuring polarized light microscopy, cryogenic scanning electron microscopy, X-ray diffraction, differential scanning calorimetry, and oscillatory rheology. Oleogel crystallization was performed in a lab-scale vessel and was monitored using light turbidimetry as an in situ technique. Results showed that the concentration of cocoa butter in sunflower oil was the parameter that affected most strongly the foamability and rheology of oleofoam samples. The size and shape of cocoa butter crystals within the oleogel was found to have a less significant effect since crystals were broken or partially melted during the aeration process. Oleofoams whipped from oleogels containing 15 and 22% w/w cocoa butter displayed an overrun of 200%, corresponding to a calorific density reduction to one-third, and an increase in both the elastic and viscous moduli compared to their oleogel precursor. This was explained by a structuring effect caused by the aeration process, where cocoa butter β(V) crystal nanoplatelets (CNPs) in the oleogel rearranged to stabilize the air bubbles via a Pickering mechanism. Oleofoams prepared from 30% w/w cocoa butter oleogels, on the other hand, incorporated less air (overrun between 150 and 180%) and displayed a similar viscoelastic profile to their unwhipped precursors potentially due to air incorporation being limited by the relatively high elastic modulus of the parent oleogels. Nevertheless, the calorific density of these samples was reduced by a factor of 1.6–2.5 compared to their full-fat analogues.