We investigate the role of viscosities on the formation of double emulsion in a microfluidic step emulsification system. Aqueous droplets of various viscosities and sizes were engulfed in fluorocarbon oil and subsequently transformed into double droplets in the microfluidic step emulsifying device. We identify two distinct regimes of double droplet formation: (i) core droplets split into multiple smaller droplets, or (ii) cores slip whole into the forming oil shell. We show that the viscosity ratio of the core and shell phases plays a crucial role in determining the mode of formation of the double emulsions. Finally, we demonstrate that high viscosity of the core droplet allows for generation of double emulsions with constant shell thickness for cores of various sizes.