Heat 1/4 cup oil and the garlic in a medium saucepan over medium heat until garlic is fragrant, about 1 minute.
Add 6 cups water; bring to a boil. Whisking constantly, add cornmeal in a slow, steady stream. Reduce heat to medium; cook, stirring occasionally, until soup has thickened slightly, about 8 minutes. Add cheese and 1/4 cup oil; cook, stirring, until oil is incorporated, about 1 minute. Stir in spinach and salt; cook, stirring, until spinach is bright green and wilted, about 1 minute more.
Divide soup among four bowls; drizzle each serving with 1 teaspoon oil. Season soup with pepper, and serve with lemon wedges.