Heat the oil in a large, deep skillet over medium heat. Add the eggplant and onion and cook while stirring until the eggplant is softened and just cooked through, about 10 minutes. Increase heat to medium-high, add the tomatoes, garlic, and salt, and cook while stirring until the garlic is fragrant, about 2 minutes.

Meanwhile, in a large saucepan, boil linguine in (salted) water per package directions, about 8 minutes. Drain the linguine, reserving 1/4 cup of the pasta cooking liquid.

Add the drained linguine and desired amount of the reserved pasta cooking liquid to the skillet with the eggplant mixture over medium-high heat, and toss with tongs to combine.

Transfer to bowls, sprinkle with the goat cheese and mint, and serve.