Bring the milk and 2 cups water to a simmer in a medium saucepan over low heat.
Meanwhile, heat the oil in a large cast-iron skillet over medium-high heat. Once the oil starts to shimmer, add the andouille and spread out into a single layer. Cook until browned on the first side, 2 to 3 minutes. Use tongs to flip the sausage pieces and cook until browned on the second side, 2 to 3 minutes more. Use tongs or a slotted spoon to transfer the sausage to a medium bowl and cover with foil to keep warm.
Add the bell pepper and a pinch of salt and pepper and cook, stirring occasionally, until tender and browned in spots, about 3 minutes. Add a drizzle more of oil if the pan seems too dry.
Transfer to a medium bowl and cover with foil to keep warm. Add the tomatoes and cook, without moving, until the tomatoes are browned on their bottoms and the skins on some are starting to burst, about 2 minutes; add a drizzle of oil if the pan seems too dry. Shake the skillet from side to side several times to turn the tomatoes and cook, shaking the pan frequently to keep the tomatoes moving, until the skins on all of the tomatoes have burst, about 2 minutes more. Transfer the tomatoes to the same bowl as the bell pepper, then season with salt and pepper and stir gently to combine.
By this time, the milk and water should have come to a simmer. Slowly whisk in the polenta, and a pinch of salt and pepper then continue whisking until the polenta has thickened and just pulls from the sides of the saucepan, about 5 minutes. Turn off the heat and stir in the butter and Cheddar until melted, about 1 minute. Season to taste with additional salt and pepper if needed. If you would like the polenta looser, whisk in 1/4 to 1/2 cup warm water.
Divide the polenta among 4 bowls and top with the andouille sausage, bell pepper and tomatoes. Garnish with the scallions and serve with hot sauce on the side.