Cut cucumber crosswise into 4" thick pieces. Using a rolling pin or the flat side of a chef’s knife, lightly crush cucumbers, then slice crosswise into 1⁄2" thick slices; then in half again.
Heat oil in a large skillet (cast iron is best), on high. Add beef and a pinch of salt; break up meat into small pieces with a wooden spoon then spread to create a single layer. Cook, undisturbed, until bottom side is browned and crisp, about 6-8 minutes. Break up meat and turn over pieces. Cook until other side is browned and crisp, and meat is cooked through, another 6–8 minutes. Remove meat to a plate, add garlic and chile peppers to same pan. Cook, stirring often, until fragrant and softened, about 1 minute. Add garlic and chile peppers to plate with meat.
Add shallots and reserved cucumbers and cook, tossing occasionally and scraping up any browned bits, until cucumbers are softened and translucent, about 6 minutes. Stir in vinegar, soy sauce, and sugar and continue cooking over medium heat, return meat, garlic and chile peppers to pan, mix together and cook until sauce is reduced slightly and meat is reheated about 2-4 minutes. Season with salt and pepper to taste.
Spoon over rice or noodles and top with herbs. Serve with lime wedges on the side.