Allow the cream cheese to come to room temperature by cutting it into pieces and leaving it out while you prepare the rest.
Chop the onion finely and mince the garlic cloves. Cut the chicken thighs into bite-sized pieces and season with 1 teaspoon kosher salt.
Set your Instant Pot to the sauté setting on high and heat the olive oil until hot and shimmering. Add the diced onion and garlic and sauté, stirring occasionally, until they are soft, about 3 minutes. Turn off the sauté function.
Add the seasoned chicken pieces to the pot and mix them gently with the softened onions. Sprinkle the rice evenly over the chicken followed by the remaining 1/2 teaspoon kosher salt. In a separate bowl, whisk together the chicken broth and Dijon mustard, then carefully pour the mixture over the rice without stirring.
Secure the lid of the Instant Pot and lock it, ensuring the valve is set to seal. Cook at high pressure for 10 minutes. It will take approximately 12 minutes for the pot to reach pressure.
While the dish cooks, grate the sharp cheddar cheese using the large holes of a box grater.
As soon as the cooking time finishes, perform a quick release of the pressure to open the lid safely.
Add the cream cheese, shredded cheddar cheese, and frozen peas and carrots to the pot. Stir gently to incorporate everything. Let the dish rest for 5 minutes to allow the cheeses to melt and flavors to meld, then stir once more until creamy and well combined before serving.