Prepare Zucchini - Place zucchini cubes in a colander in the sink. Sprinkle with salt, lightly toss, and let sit for 30 minutes. When done, rinse Zucchini thoroughly and dry well with paper towels.
Fry Vegetables - About 10 minutes before zucchini's done "sweating", heat butter and oil in a large skillet over medium-low heat. Add garlic slices and cook, stirring, until golden brown, about 3 minutes. Be careful not to burn the garlic or it will turn bitter and ruin the dish. Remove pan from heat and pour into a fine-mesh strainer set over a small bowl. Set garlic aside and pour drained butter-oil in the bowl back into pan and turn heat to medium-high. Add zucchini and cook, stirring, until browned and tender but still a little crunchy, about 8-10 minutes. Remove pan from heat.
Finish Dish - Squeeze lime juice over zucchini in the pan, add toasted garlic slices and toss. Add salt and pepper, oregano, and parsley. Mix and add more salt if necessary. Pour into a warm bowl and serve.