In a small bowl, combine the dijon mustard, mayonnaise, almond milk, and salt and black pepper to taste for the almond-mustard sauce. Whisk until smooth. Thin out if necessary and transfer to an airtight container. Refrigerate until you are ready to use.
In a medium bowl, combine the breadcrumbs, parsley, green onions, mayonnaise, lemon juice, salt, black pepper and eggs. Mix until fully combined and moist. Gently fold in the crabmeat.
Form the crab cake mixture into 4 equal sized patties. Set aside.
In a large nonstick sauté pan set over medium-high heat, add the vegetable oil and butter. Swirl until the butter has melted and then add each of the patties. Cook for about 5 minutes on each side or under brown and crispy. Transfer the crab cakes to a plate that has been lined with a paper towel.
Prepare your eggs to your liking. Serve the crab cakes on a bed of fresh greens. Top with eggs and sprinkle with fresh parsley. Serve the almond-mustard sauce on the side. Enjoy immediately!