Combine kosher salt and boiling water in a large bowl; stir to dissolve. Add cold water and chicken strips. Refrigerate 30 minutes to 1 hour. Drain and pat chicken dry before cooking.
Use a mandoline to cut zucchini into slices 1/8-inch thick. Cut slices into strips about the thickness of fettuccine. Place zucchini in a bowl and sprinkle with 2 tablespoons salt to cover. Leave for 30 minute to soften.
Heat oil in a skillet over medium heat. Add chicken; cook until browned on all sides, no longer pink inside, and juices run clear, 5 to 7 minutes. Transfer cooked chicken to a bowl.
Add butter to the same skillet over high heat. Crush garlic directly into skillet. Add cream and bring to a boil. Reduce heat to medium-low and add Parmesan cheese. Whisk continuously until fully melted, about 2 minutes. Add pepper. Add zucchini strips to the skillet; cook and stir for 1 to 2 minutes.
Return cooked chicken to the skillet; cook until warmed through, about 1 minute more. Toss well to coat. Season with salt and pepper. Garnish with tomatoes.
