Prepare beans: Heat oil in a medium saucepan over medium heat. Saute garlic and shallot until tender, about 5 minutes. Add oregano and beans (with their liquid) and bring to a boil. Mash beans with the back of a wooden spoon and cook until slightly thickened, 2 to 4 minutes. Season with salt and pepper.
Spread 1/2 cup beans on wrap. Layer with cottage cheese, avocado, jalapenos, and cilantro. Fold wrap to seal.