Cook wild rice + ¼ teaspoon and ⅛ teaspoon salt in a large pot of boiling water according to the cooking instructions on the package (usually, wild rice cooks about 45 minutes, so plan accordingly).
When wild rice is almost cooked, heat olive oil in a large skillet on medium-high heat. Add minced garlic, finely grated carrots, and cook, stirring, for about 1 minute, until carrots start to soften.
Add chopped chicken, sprinkle with ¼ teaspoon salt and ¼ teaspoon pepper, and cook on medium heat for about 5 minutes, stirring occasionally, until the chicken is cooked through.
Add 1 cup green peas (I used the frozen ones). You can add them either frozen or thawed. Stir them in and mix with chicken-carrot mixture.
When the wild rice is done, add cooked wild rice to the skillet with the chicken and mix everything.
Add 1 cup half and half, ⅓ cup chicken broth to the skillet with the chicken and rice and bring to boil. Add ½ cup shredded Parmesan cheese. Stir, until the cheese has melted, on medium-low heat. Taste and add more salt if needed, about ⅛ teaspoon or ¼ teaspoon more.