The two sentences that use an adverbial clause are:
C. Javy was named captain of the team despite it being his first year on the team. (Although this could be misleading, "despite" sets a condition, but there's no traditional adverbial clause here.) E. So that we would have enough left for tomorrow, we only used half of the vegetables in the salad. (This contains an adverbial clause: "So that we would have enough left for tomorrow.")
While option C involves a phrase that provides context, it doesn't strictly contain an adverbial clause as defined traditionally. Thus, based on clarity, the true answer is:
E. So that we would have enough left for tomorrow, we only used half of the vegetables in the salad.