Penne with Treviso and Goat Cheese

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1 pound penne pasta

1/4 cup extra-virgin olive oil

1 clove garlic, halved

1 pound treviso or radicchio, chopped (about 4 cups)

3 packed cups (3 ounces) baby spinach

1/2 cup low-sodium chicken stock

1/4 cup balsamic vinegar

2 tablespoons fresh lemon juice

1 tablespoon kosher salt, plus more for seasoning

1/2 teaspoon red pepper flakes

1 1/2 cups grated Parmesan

1 1/2 cups (11 ounces) goat cheese, crumbled

1/2 cup basil leaves, torn