Given that you shouldn't put leftovers of meals that has touched meat in compost bins due to the risk of attracting vermin, what is the most sustainable way to deal with these scraps?
Get a pig. Or some chickens. You still need to follow some hygiene rules before feeding them meat scraps, check your local agri/health advisory office.
Are you on a biodynamic septic system? Flush them. The bacteria should chew them up happily.
The most sustainable way is reuse. Perhaps you can eat the leftovers later, or use it as ingredients for soup.
As others have also suggested here, you can feed leftovers to animals if you have them (like a dog, chickens or pigs). But be warned that local regulations may not allow this! For example in the EU you are not allowed to feed kitchen scraps from an 'unregulated' kitchen to farm animals like chickens and pigs. Also not all leftovers may be healthy for your animals. For example raw meat is bad for all animals because of the risk of bacterial contamination, avocado is poisonous to chickens, and chocolate and unions are very bad for dogs.
If you cannot eat it anymore, I recommend composting in a closed compost bin with small air-holes so vermin cannot enter. If the leftovers contain much grease and salt, then normal composting can be slow and smelly. A closed bin can reduce the smell, but in this case it would be even better to do bokashi composting. With Bokashi you 'pre-process' the materials in a airtight bin with micro-organisms. After 2 weeks you can safely compost the materials further on a regular compost heap or bury it in your garden. The only downside is that you have to buy or create your own effective micro-organisms.
Pigs & chickens. The chickens follow the pig for all left.