Bring the milk and water to a simmer in a heavy saucepan over medium heat. Whisk in the cornmeal in a slow stream so no lumps form.
Lower the heat to low and cook, stirring every minute with a wooden spoon, until thick and creamy, about 15 minutes. Cover and keep warm; it bubbles and spits, so stand back.
Stir the cheddar and salt into the polenta. Add a splash of hot water if it gets too stiff.
Heat the oil in a large skillet over medium heat. Cook the diced pepper and garlic for 2 minutes.
Turn to medium-high, add the shrimp, smoked paprika and cayenne and cook for about 3 minutes, turning once, until pink and opaque all the way through.
Spoon the polenta into bowls, top with the shrimp and finish with lemon juice and sliced green onion.