I think you are referring to a dish called ropa vieja -- "old clothes," but it isnt fried, it's cooked in a sauce. If that doesnt sound right, then forget it. There is a cuban restaurant here that serves it, but I have never seen it in Dominican restaurants. I could be wrong though. There is another cuban dish that I like to cook, Picadillo: you take ground beef, tomatoes, onions, garlic, sazon, a few tubers or veggies or what ever you like to add to such stews, a couple cloves, raisins and olives. Delicious!
Grease can be a problem here. Dominican food neednt be so greasy, and you can bake instead of fry some of these items, but in general there is a lot of fried food here. If you dont like pork or seafood, you still have chicken, plenty of that, and carne de res (beef).
Here is a basic recipe for sazon, which can be tossed into a variety of dishes to make them taste great. No need for bouillon cubes.
3 md Onions; chopped
1 or 2 cubanela peppers
1 red bell pepper
4 lg Garlic cloves; peeled, mashed -- or more if you like
1 Tb Oregano
1 Tb Curry powder (optional)
1 bunch Scallions; chopped, all of it, green and white parts
1 bunch cilantro -- the broad leaf, not cilantrico
2 stalks celery
A few splashes of Tabasco or other hot sauce, or just a red pepper sauce like the Vietnamese style (also optional if you dont like spicey food)
1 tb Paprika, sweet
About a half cup Tomato paste, or maybe less, to taste
1 c Oil, olive
1/2 c Vinegar, white
booze! Vermouth, wine, rum, whatever you like. About a half cup.
Salt, black pepper; to taste
You take all this and place it in a blender. Once blended, you cook it in a saucepan so that it simmers for about five minutes, place the sauce in clean jars, refrigerate. lasts a good while.