Phase 1: Prepare and Cook the Chicken

1. Prepare Chicken: Pat the cut chicken pieces dry with paper towels (this helps them brown better). In a medium bowl or a shallow dish, combine the 1/4 cup of all-purpose flour, 1/2 teaspoon of salt, and 1/4 teaspoon of black pepper. Add the chicken pieces and toss to coat them evenly. Shake off any excess flour.
2. Brown the Chicken: Heat 1 tablespoon of olive oil and 1 tablespoon of butter in a large, heavy-bottomed skillet or Dutch oven over medium-high heat. Once the butter is melted and the oil is shimmering, add half of the floured chicken pieces in a single layer. Be careful not to overcrowd the pan, as this will cause the chicken to steam rather than brown.
3. Cook in Batches: Cook the chicken for 3-4 minutes per side, until golden brown and cooked through. Remove the cooked chicken from the skillet with a slotted spoon and set it aside on a plate. Repeat with the remaining chicken, adding more oil/butter if the pan looks dry.

Phase 2: Sauté Aromatics and Mushrooms

1. Sauté Onions: To the same skillet (do not wipe it clean – those browned bits are flavor!), add the remaining 1 tablespoon of olive oil and 1 tablespoon of butter if needed. Add the chopped yellow onion and sauté over medium heat for about 4-5 minutes, or until softened and translucent.
2. Cook Mushrooms: Add the sliced mushrooms to the skillet. Increase the heat slightly to medium-high. Cook the mushrooms, stirring occasionally, for 5-7 minutes, or until they have released their liquid, the liquid has evaporated, and the mushrooms are nicely browned and slightly caramelized. Season them with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper during this process.
3. Add Garlic: Stir in the minced garlic and cook for another minute until fragrant. Be careful not to burn the garlic.

Phase 3: Build the Sauce

1. Deglaze (Optional but Recommended): If using, pour the 1/4 cup of dry white wine into the skillet. Scrape up any browned bits (fond) from the bottom of the pan with a wooden spoon or spatula. Let the wine simmer and reduce by about half, which should take 1-2 minutes.
2. Add Liquids and Seasonings: Stir in the 1 tablespoon of Dijon mustard, 1 teaspoon of smoked paprika, and 1 teaspoon of Worcestershire sauce. Cook for 30 seconds, stirring constantly, until fragrant.
3. Pour in Broth: Gradually pour in the 1.5 cups of chicken broth, stirring continuously to combine. Bring the mixture to a gentle simmer.
4. Simmer and Thicken: Reduce the heat to low and let the sauce simmer gently for 5-7 minutes, allowing it to thicken slightly. If it’s not thickening as much as you’d like, you can mix 1 tablespoon of cornstarch with 2 tablespoons of cold water to make a slurry, then whisk it into the sauce and simmer for another minute or two until thickened.

Phase 4: Combine and Finish

1. Return Chicken to Pan: Add the cooked chicken (and any accumulated juices from the plate) back into the skillet with the sauce. Stir to combine and let it heat through for a couple of minutes.
2. Temper and Add Sour Cream: Turn off the heat completely (or reduce to the lowest possible setting). Take the 3/4 cup of room temperature sour cream. To prevent it from curdling, you can temper it: whisk a few tablespoons of the hot sauce from the skillet into the sour cream in a separate small bowl, then pour this tempered mixture back into the skillet. Stir gently until the sour cream is fully incorporated and the sauce is smooth and creamy. Do not let the sauce boil after adding the sour cream.
3. Taste and Adjust: Taste the Stroganoff and adjust seasonings if necessary (more salt, pepper, or a tiny splash of lemon juice for brightness if desired).
4. Garnish and Serve: Stir in most of the freshly chopped parsley or dill, reserving some for garnish. Serve immediately over hot cooked egg noodles, rice, or mashed potatoes. Garnish with the remaining fresh herbs.