Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. Drain and reserve about 1 cup of the pasta water.
In a 12-inch skillet, heat the oil over medium heat. Add the garlic and cook until fragrant and golden, about 1 minute. Remove the garlic and discard.
Add the treviso, spinach, chicken stock, balsamic vinegar, lemon juice, 1 tablespoon of salt, and red pepper flakes. Cook until the treviso and spinach until wilted, about 6 to 8 minutes.
Add the pasta and Parmesan. Toss well and thin out the sauce with a little pasta water, if needed. Season with salt, to taste.
Transfer the penne to serving bowls. Top each portion with the crumbled goat cheese and garnish with basil before serving.
Recipe courtesy of Giada De Laurentiis