Chicken with Garlic and Parmesan Polenta

Name: Chicken with Garlic and Parmesan Polenta
Ingredients: 3 Tablespoons butter; 4 large cloves garlic, minced; 2 Tablespoons minced rosemary; 1 1/4 Cup water; 1 Cup milk, plus more as needed; One 14 ½-ounce can chicken broth; Salt and pepper, to taste; 1 Cup yellow cornmeal; 1/3 Cup grated Parmesan; 4 large chicken thighs; 3 1/2 Tablespoons butter; 2 sprigs rosemary, plus more for garnish; Generous pinch of nutmeg; 1 Cup chicken broth; 1/2 Cup rum (optional); 2 Roma tomatoes, sliced, for garnish; 1 cucumber, sliced, for garnish