In a medium size saucepan over medium heat, add one tablespoon of olive oil. Once the pan is hot, add the peppers and saute about 5-10 minutes until the skin of the pepper begins to char. Once done, remove from pan and set aside.
Next, add remaining tablespoon of olive oil to the pan and increase heat to medium high. Add diced chicken and cook until done, about 5-10 minutes, depending on the size of the pieces. Once cooked, remove from pan and set aside.
In a small bowl, dissolve the tomato paste into the vodka, stir until smooth and set aside to be added to the sauce.
Reduce heat on pan to medium low and add butter and minced garlic. Cook until garlic is fragrant, about a minute or two.
Next, add the cream to the pan and stir to combine the cream and butter.
Once the cream and butter are combine, add the tomato paste and vodka mixture, basil, Parmesan cheese, red pepper flakes, salt and pepper. Cook until most of the alcohol has evaporated and this sauce has thickened, about 5 minutes.
Lastly, add in chicken, red peppers and spinach, mix to combine. Cook a few additional minutes until spinach has wilted and the dish is ready to be served!