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Step 1
Combine milk and chicken broth in a medium pot and bring to a boil.
Step 2
Slowly stir in polenta. Return to a simmer, then reduce heat to medium low. Cook, stirring frequently, until polenta is fully cooked. Refer to cooking time on package, as it can vary quite a bit depending on the coarseness of the polenta.
Step 3
Remove from heat and stir in parmesan cheese until melted. Note that the polenta will thicken as it sits, you can always stir in a little water or milk if needed.
Step 4
Meanwhile, heat 1 tablespoon olive oil in a skillet over medium high heat. Season the shrimp with salt and pepper, then sauté until cooked through, about 5 minutes. Remove to a plate.
Step 5
Add remaining 3 tablespoons of oil, and once hot add the garlic and red chili flakes. Cook for 1 minute, then add in cherry tomatoes. Cook for 3 minutes.
Step 6
Add in wine, chicken broth, thyme and basil. Bring to a simmer, reduce heat to medium, and cook for 10 minutes.
Step 7
Add shrimp and butter. Stir until well combined. Cook for 2-3 minutes. Taste and adjust for salt.
Step 8
Divide polenta into four bowls and top with shrimp mixture. Garnish with additional basil leaves and serve immediately.