While the lentils are cooking, add butter to a large skillet over medium heat. Once melted, add the shallots and sauté for 4-5 minutes. Add in the garlic and continue cooking for 2-3 minutes.
Add in mushrooms, celery, carrots, parsley, thyme, salt, and pepper. Cook for 7-8 minutes until the vegetables begin to soften. Increase the heat to medium high and cook for additional 4-5 minutes.
Add in the dijon mustard, cooked lentils, and the breadcrumbs. Stir well and cook for 7-8 more minutes, stirring several times. Remove from heat and let cool. (For best results, refrigerate the mixture for ~1 hour.)
Divide the filling mixture in half. Place one sheet of puff pastry on a cutting board. Shape the filling into an oval on one of the short ends of the puff pastry, leaving 1-2 inches of space around the border.
Fold the puff pastry over the filling. Trim off most of the excess – you should only have enough to just tuck the puff pastry under the filling so it doesn't burst open while cooking. Pinch the seam together.
Score the top of each wellington with a knife. Brush with nondairy milk and (optional) sprinkle with some flaky salt. Bake for 50-55 minutes until the puff pastry is golden brown. Let cool at least 30 minutes before slicing.