Add olive oil to a large skillet over medium heat. Add chicken breasts and cook, uncovered, for 5 minutes. Flip chicken and cook for an additional 5 minutes so that both sides of chicken are opaque and golden. Turn chicken again and then cover the skillet. Reduce heat to medium and cook chicken, covered, for 10 minutes. When done, remove chicken from skillet and set on a plate.
Increase heat back to medium. If needed, add more olive oil to the skillet. Add chopped leek to skillet and cook until leek is tender and translucent, about 4-6 minutes.
Add minced garlic to skillet and cook until garlic is golden and fragrant, about 1 minute.
Pour in heavy whipping cream, mustard, dijon mustard, and lemon juice. Season sauce with salt and pepper to taste. Allow mixture to simmer for another 3 minutes, stirring constantly.
Add chicken back to the skillet and toss in the creamy dijon sauce to coat. Continue to stir and coat chicken until chicken is heated through, about another 2-3 minutes.
Remove skillet from heat and sprinkle the tops of chicken with fresh parsley. Serve immediately.