Ethyl tert-butyl ether is treated with one equivalent of cold, concentrated HI. The products are

The ether oxygen is protonated first. With a tertiary alkyl group the C-O bond breaks through an $S_N1$ path because the tertiary cation $\mathrm{(CH_3)_3C^+}$ is stable; iodide then attacks it, giving $\mathrm{(CH_3)_3CI}$ and ethanol. With one equivalent of $\mathrm{HI}$ in the cold the ethanol is not converted further. Cleavage by $S_N2$ at the ethyl carbon (giving $\mathrm{C_2H_5I}$) occurs only when both groups are primary or methyl.