If you are restricted to 10-15 minutes a day, it might be hard to compensate for a huge calory surplus. You should ask for smaller portions or (while I don't want to encourage food waste) just refuse to eat up your meal if they deny to give you a suitable portion.
Having said that, you can certainly increase your calory consumption with exercises. 10-15 minutes is not much, but neither nothing. Being restricted to 10-15 minutes you might get the best price-performance ratio with HIIT, imho. HIIT has been shown to have more impact on body recomposition, health and fitness than steady state exercise (see here for example, if you are a student you might also be able to access this meta-analysis or this study). Here is a short summary of the findings.
Some examples of exercises you can perform
- Burpees (or sprawls if you're having issues with the push-up part)
- Mountain climbers
If you have access to a home trainer that would be an option, too.