Preheat oven to 350 degrees F (175 degrees C). Grease a baking dish or line a baking sheet with parchment paper.
Cut each zucchini into 3 equal sections and scoop out the center core of each, leaving about 1/2 inch of zucchini on the bottom. Finely chop the removed core and place in a bowl.
Heat oil in a skillet over medium heat and cook onion until soft and translucent, about 5 minutes. Add tomatoes, season with salt, and cook for for 5 minutes. Stir in carrot and reserved zucchini core and mix well. Season with garlic, oregano, salt, and pepper and cook for 2 to 3 minutes. Remove from heat and stir crumbled goat cheese into vegetable filling.
Spoon vegetable filling into hollowed-out zucchini pieces and set into prepared baking dish or baking sheet.
Bake in the preheated oven until zucchini are soft, 30 to 35 minutes.