3 cups chicken or vegetable broth, or water
3 cups whole milk
2 cups quick-cooking polenta (such as Bob's Red Mill)
1 ½ cups (6 oz.) grated Parmigiano-Reggiano and/or Pecorino
2 tbsp. EVOO, plus more for drizzling, or good butter
1 tbsp. coarsely ground black pepper
2 tsp. honey plus some to drizzle
¾ cup drained semi-dried tomatoes, chopped
Nonaerosol cooking spray
6 cups baby or wild arugula
1 lemon, halved
¼ cup celery leaves or fresh parsley, chopped
Heat the broth or water and milk in a large saucepot until boiling. Whisk in polenta. Reduce heat to medium-low and continue whisking for 2 to 3 minutes, until smooth and creamy; remove from heat. Stir in cheese, EVOO or butter, black pepper, and honey until combined. Season with salt, then fold in tomatoes. Transfer to a parchment-lined 17-by-10-inch baking pan or two 9-by-9-inch baking dishes, spreading into an even layer. Set in freezer to chill for 15 minutes.
Heat a 12-inch cast-iron skillet or nonstick pan over medium heat. Cut the firm polenta into 12 equal slices and use your hands to make free-form fritters about the size of your palm (about 3 inches in diameter). Spray one side of the fritters generously with cooking spray and place 6 in pan sprayed-side down. Fry until golden, 2 to 3 minutes; spray the top side of the fritters, then flip and cook for 2 to 3 more minutes, until golden. Repeat with remaining fritters. Transfer to a wire rack or a paper-towel- lined plate.
Toss arugula with juice of half the lemon, a drizzle of EVOO, and salt. Serve 3 fritters with arugula alongside and garnish with celery leaves or parsley. Cut remaining lemon half into small wedges and serve with meal.