Melt butter and extra-virgin olive oil in a large cast-iron skillet.
Season the chicken breasts on all sides with salt and black pepper. Add flour to a large bowl or pyrex dish. Use something large enough to fit each chicken breast, then dredge each breast through flour on both sides. Gently shake off the flour and set breasts on a large platter or baking sheet.
Add the breasts to the skillet and cook about 4-5 minutes per side, until golden brown.
Remove chicken and set aside on a platter. Add leeks, shallots, and 1-2 tablespoons butter to the skillet and sauté for a few minutes until softened. Then add the garlic and sauté for an additional 1-2 minutes. It’s important to add the garlic at the end, so it doesn’t burn. You only want to sauté until it’s fragrant and you can smell the garlic.
Deglaze the pan with red wine, stirring with a wooden spoon to loosen up any browned bits at the bottom of the pan. Those brown bits (also called fond) are going to add to the flavor of the sauce. Let everything reduce for about 5 minutes, only until the wine is reduced by half.
Stir in the tomato paste and cook 3-5 minutes until it deepens in color. Then add heavy cream, bring to a boil and then simmer until the sauce thickens.
Stir in fresh baby spinach and sun-dried tomatoes and simmer gently. The sauce will thicken a bit more. Taste and adjust seasoning if necessary. This would be the time to add red pepper flakes if you want a bit of heat.
When the sauce tastes exactly as you like, add the chicken back to the pan and continue to cook until the chicken is cooked through to 165 degrees. One of my most used kitchen gadgets is a digital meat thermometer. I seriously don’t know what I would do without it!! It will ensure your meat is always cooked to the perfect temperature.
Serve immediately over rice or couscous!