We present a robust way to create multiple emulsions with controllable shell thicknesses that can vary over a wide range. We use a microfluidic device to create a coaxial jet of immiscible fluids; using a dripping instability, we break the jet into multiple emulsions. By controlling the thickness of each layer of the jet, we adjust the thicknesses of the shells of the multiple emulsions. The same method is also effective in creating monodisperse emulsions from fluids that cannot otherwise be controllably emulsified, such as, for example, viscoelastic fluids.