If using wild rice, place the wild rice in a medium saucepan. Add 2 1/2 cups of water. Bring to a boil, then cover and reduce the heat to medium low. Simmer the rice for 30-45 minutes. Drain off any excess water and set the rice aside.
If using a long grain and wild rice mix, discard or find another use for the accompanying seasoning packet and cook the rice according to package directions.
Heat the oil in a large pot over medium heat. Working in batches, add the smoked sausage and sauté until the sausage starts to turn brown and crisp around the edges, about 10 minutes. Remove the sausage with a slotted spoon as set aside on paper towels to drain. Drain all but one tablespoon of the grease from the pot.
Add the carrots and onions to the pot. Sauté until the onions become soft and translucent, about 5-6 minutes.
Add the garlic and frozen corn kernels. Sauté for 30 seconds.
Gradually add the flour, stirring until the vegetables are coated and there are no large clumps. Cook for three minutes, stirring constantly to prevent the flour from burning.
Add the chicken broth. Bring the chowder to a boil, then reduce the heat to a simmer and cook until the mixture begins to thicken, about 12 minutes.
Stir in the whole milk, rice and cooked sausage. Cook until the mixture thickens again, about 5-10 minutes.
Season with salt and pepper to taste.