I'd like to think that Adobo is national 'way of cooking' rather than the national dish of the Philippines. You may be familiar with chicken or pork adobo -- meat that is boiled then simmered in a mixture of vinegar and soy sauce, and then some, like garlic, bay leaves and black peppercorn. I've said before that there are as many versions of Adobo as the number of islands in the archipelago -- all 7,100 of them.
Vegetarian? No problem. You can prepare Adobo without the meat, using meatless ingredients. Like Shiitake mushrooms. I believe that Shiitake mushrooms are the best meatless ingredient to use only because of their texture which has the consistency of pork or chicken. And with proper attention to your cooking, the mushrooms can be tender and juicy, just liked how most people like their Adobo.