The sentences that use an adverbial clause are:
- Javy was named captain of the team despite it being his first year on the team.
- So that we would have enough left for tomorrow, we only used half of the vegetables in the salad.
The second sentence clearly includes an adverbial clause ("So that we would have enough left for tomorrow"), which expresses the purpose of the action. The first sentence also contains a phrase that functions somewhat like an adverbial clause, but it's less direct. If you're strictly looking for traditional adverbial clauses, the clear choice here would just be the second sentence.