In a 10-inch straight-sided saute pan, heat 2 teaspoons of the oil over medium-high heat. Add the mushrooms, season generously with salt, and cook undisturbed until well browned on one side, 1 to 3 minutes. Add half of the shallot and 1/2 Tbs. of the sage to the pan and continue to cook, stirring, until the mushrooms are well browned all over, another 3 to 5 minutes. Season generously with black pepper and transfer to a bowl. Leave the pan off the heat.
Generously season the chicken thighs with salt and pepper. Return the pan to medium-high heat, add the remaining 2 teaspoons oil, and swirl to coat the pan. Add the chicken and cook undisturbed for 1 minute. Add 1/2 Tbs. of the garlic, 1/2 Tbs. of the sage, and the remaining shallot and continue to cook, stirring, until the chicken is no longer pink on the outside, 2 to 4 minutes. Add the mushrooms, sherry, and red pepper and cook to reduce the sherry slightly, about 2 minutes.
Lower the heat to medium and stir in the sour cream, tomato, and the remaining garlic. Partially cover the pan and simmer until the chicken is cooked through, 15 to 20 minutes. If the sauce seems overly thick, thin it with a little water. Season to taste with more salt and pepper. Serve sprinkled with the remaining sage.