Add olive oil to a large skillet and warm over medium heat.

Add the sliced kielbasa and diced onion to the skillet and cook for about 4 minutes until lightly browned.

Stir in the minced garlic and Italian seasoning; cook for 30 seconds while stirring constantly.

Pour in the chicken broth, diced tomatoes, milk, pasta, and ground black pepper. Stir to combine.

Bring the mixture to a boil. Once boiling, reduce heat to medium-low, cover, and cook for 15 minutes until the pasta is al dente, stirring occasionally.

Remove from heat and stir in the Cheddar-Jack cheese until fully melted and incorporated.

Adjust seasoning with salt and pepper as desired before serving.