In a medium skillet, over low-medium heat, add oil. Sauté onions, garlic, mixed veggies, and green onions. Remove from the pan and set aside.
Add eggs into skillet and scramble. Chop into small pieces, remove from the pan, and set aside.
Cook rice according to package directions and set aside.
In a large skillet, melt butter over low-medium heat. Add in steak, rice, eggs, vegetables, sesame seeds, pepper, and soy sauce. Mix well.
Cook over low-medium heat, stirring occasionally until heated through. Set aside.
Take one egg roll wrapper at a time, brush around the edges with water, add a heaping tablespoon of rice into the center of the wrapper (wrapper is diagonal).
Start out by folding both outer edges inward over the mixture, next fold the bottom edge over the mixture, and roll to seal.
Continue until all wrappers have been filled and rolled.