Step 1: Concept
This is a Williamson Ether Synthesis, which follows an $S_N2$ mechanism.
Step 2: Analysis
The reagents are a $1^\circ$ alkyl halide (methyl bromide) and a bulky alkoxide (potassium tert-butoxide).
Step 3: Mechanism
Bulky alkoxides favor elimination ($E2$) with hindered halides, but since the halide is methyl (least hindered), substitution ($S_N2$) occurs to form the ether.
Step 4: Conclusion
The product is tert-butyl methyl ether.
Final Answer:(D)