Preheat oven to 400 degrees. Line a baking sheet with parchment paper or use a silicone mat.
Add oil to a skillet over medium heat. Add carrot, spinach/kale, and minced garlic. Cook until veggies begin to soften and the garlic is golden brown. If using kale, add a 1/4 cup of water to the pan and cook until water has evaporated and kale is soft. Season veggie mixture with a large pinch of salt and the lemon juice. Transfer to a bowl and set aside to cool.
Mix mustard and honey together in a small bowl. Cut the salmon into 8 equal pieces and place them on a plate.
Unroll one sheet of puff pastry on a work surface and cut it into 8 equal rectangles. I like to use a pizza wheel. Divide the cooked veggie mixture between the 8 pastry rectangles, leaving a border of the pastry uncovered. Place a piece of salmon on top of the veggies. Sprinkle each salmon piece with a pinch of salt then spread the honey-mustard over the surface.
Unroll the second sheet of puff pastry and cut it into 8 equal rectangles as you did with the first piece. Place a piece of the pastry on top of each piece of salmon to create a package. If the salmon is thick, you may need to stretch the second piece of pastry a little to fit. Press the edges of the pastry together to seal.
At this point, you can make a decorative edge by pressing a fork all around the edges of the pastry or make a fish-shaped pastry. To make a fish, use a pairing knife to cut a fish shape around the pastry (see pictures above). Roll some of the excess pastry into a small eyeball and place that on the fish then use the tip of your knife to make semi-circles along the fish's body to make the scales. Or you can decorate the top of the pastry however you'd like. To make sure any steam inside the pastry pocket can vent, poke a small in the pastry.
Brush the beaten egg over the top of each of the pastry bundles. Bake until golden brown, 15 to 18 minutes. Serve warm.