Preheat the oven to 400°. Line a baking sheet with parchment paper or a silicone mat. Slice the tip of the stem off of each carrot and lightly peel (if desired). Arrange on the baking mat, spray with high heat cooking spray (or oil), sprinkle with salt then bake in the oven for 25-30 minutes, or until soft. Set aside to cool.
In a large pot, warm the olive oil over medium heat. Add the onion and cook until translucent. Then add the mushrooms, garlic, and celery, and continue to cook for about 10 minutes, until soft. Add the balsamic vinegar and cook until most of the liquid is absorbed. Set aside to cool.
Add half of the lentils to a food processor and pulse a few times until finely chopped (if you don't have a food processor you can chop as fine as possible and it will still come out great). Place in a large bowl along with remaining cooked lentils and mushroom mixture. Add the salt, pepper, breadcrumbs, walnuts, sunflower seeds, tomato paste, tamari, oregano, and thyme. Sprinkle half of flour over top then stir to combine. Add the remaining flour and continue to mix until well combined. If mixture seems too wet, add more breadcrumbs or flour as needed. Refrigerate while you prepare the dough, for about 30 minutes.
Set then oven to 350°F. On a large sheet of parchment paper, carefully place one layer of phyllo dough on top. Brush with melted butter then carefully layer another piece on top. Continue to brush each sheet with butter and layer until you have about 12 sheets. Add one last sheet on top and do NOT brush it with butter.
Take the cooled lentil mixture from the refrigerator and layer half of it along the center of the dough, using your hands to spread it out into a rectangle about 2 to 3-inches from the edges. Arrange the carrots on top with 1 to 2-inches in between. Press them gently into the lentil mixture.
Take the remaining lentil mixture and shape into a log. Place it on top of the carrots closer to one side then gently fold the edge over top and roll like a burrito. With seam side down, brush the outside with melted butter. Cut diagonal slices into the top with about 1-inch in between. Transfer to a baking sheet (on top of parchment paper) then bake in the oven for 35-45 minutes, until outside is golden brown. Allow to cool for 5-10 minutes.
Slice individual pieces then serve warm with mushroom gravy and enjoy!
You can prepare this recipe a day ahead, wrap in plastic wrap and place in the fridge until you are ready to bake.