Trouble with enterpreting Faraday's Law

In fact, your interpretation is not 100% right.

The equation you quote (Maxwell-Faraday) is: $$nablatimesmathbf{E} = -frac{partialmathbf{B}}{partial t}$$

Then, is $bf{B}$ is steady (particularly in time as it's what is interesting in that case) then the field $bf{E}$ will have a curl equal to $0$. But $nablatimesbf{E}$ does not imply $mathbf{E}=0$. It only implies that $mathbf{E}$ is steady (but, that's true, the case $bf{E}=0$ is included in the possibilities but is not mandatory).

So, a constant and steady magnetic field can be used to create a constant and steady electic field.