Preheat oven to 375 degrees and prepare a baking sheet with foil or use a nonstick baking sheet. Thoroughly rinse produce and pat dry. Stem kale and coarsely chop the leaves. Quarter mushrooms. Peel and mince shallot. Mince garlic. Stem thyme. Rinse chicken breasts and pat dry.

Season chicken breasts with a pinch of salt and pepper. Heat 1 tsp. olive oil in a medium non-stick pan over medium-high heat. Add chicken breasts to pan and cook until golden brown, about 4-5 minutes. Turn and cook 2 more minutes. Transfer to prepared baking sheet and bake 10 minutes, or until internal temperature reaches 165 degrees. Set aside and wipe pan clean.

In a small pot, combine shallots, red wine, and vinegar. Bring to a boil and reduce liquid to 1/4 cup. Add 1 Tbsp. evaporated milk. Remove from heat and add butter 1 Tbsp. at a time, whisking constantly. Add next piece of butter only when last is completely incorporated. This is a method called "mounting" the butter and makes sauces rich and smooth. Set pot aside and season with salt and pepper. If a smooth textured sauce is desired, pass sauce through a strainer.

Heat 2 tsp. olive oil in same pan used to sear chicken over medium heat. Add half the garlic and half the thyme and cook until fragrant, about 20 seconds. Add mushrooms and a pinch of salt and cook until browned and beginning to soften, about 6-8 minutes. Transfer mushrooms to a plate and set aside. Wipe out pan and return to medium heat. Salting mushrooms while they cook will help them release their moisture and caramelize quicker.

In same pan, add 1 tsp. olive oil and remaining garlic. Cook 30 seconds and add chopped kale and remaining evaporated milk. Cook for 2-3 minutes or until evaporated milk is thick and creamy and kale is wilted. Season to taste with salt and pepper.

Arrange kale and mushrooms on a plate. Spoon sauce onto plate and place a chicken breast on top of sauce. Garnish with remaining thyme.