Since 1934, sweet-lovers have been flocking to this retailer for ice cream cakes, cones, cookies and more.. In Short Tom Carvel was inspired to found a freestanding ice cream store after his ice cream truck suffered a flat tire and he began selling his melting inventory from the roadside. Today, Carvel products can be found in grocery stores and at franchises throughout the country. Specialties include ice cream cakes in a variety of shapes for just about any occasion. Other sweet treats include ice cream cones, shakes, sandwiches and sundaes.