Heat olive oil over medium-high in a cast iron skillet . Sauté onions, carrots, and celery for 8 minutes, or until soft, stirring occasionally. Stir in the garlic, thyme, and rosemary. Cook for two minutes, stirring frequently.
Push the cooked aromatics out to the sides of the pan, creating a space in the center. Add tomato paste to the middle and cook, stirring frequently until it browns slightly. Mix in with the aromatics.
Deglaze the skillet by pouring in dry red wine. Scrape up any browned bits stuck to the bottom of the pan. Cook for about 4 minutes, or until the red wine has reduced by half.
Add vegetable broth, lentils, bay leaves, and paprika. Stir well. Bring the mixture to a boil, then reduce the heat to a rapid simmer. Cook uncovered for 25 minutes, or until the lentils are tender and most of the liquid has been absorbed.
Reduce the heat to low and stir in the soy sauce, balsamic vinegar, almond butter, and Worcestershire sauce. Stir until fully combined. Season with salt and pepper to taste. Add the peas. Set aside.
Preheat the oven to 425º F. Peel and dice the potatoes into 1-inch cubes. Add them to a large pot and cover with 1–2 inches of cold water. Season the water generously with salt, then bring it to a boil and cook until the potatoes are tender, about 15–20 minutes. Drain the potatoes well. If they still seem moist, return them to the pot over low heat for about a minute to cook off any remaining moisture.
Pass the potatoes through a fine mesh strainer into a separate bowl for a smooth texture. Stir in the melted butter, heavy cream, salt, white pepper, paprika, and nutmeg until fully combined. Let the mixture cool slightly before adding the eggs one at a time, stirring well after each yolk until fully incorporated.
Transfer the potato mixture to a piping bag fitted with a large star tip. For easier bag changes, insert the star tip into one bag, then place a second bag filled with potato mixture inside the first bag.
Spread the lentil filling evenly in your pan, then pipe the potato mixture into elegant swirls, about 1 1/2 inches wide and 1 inch tall. If there are any gaps between the swirls, fill them with small dabs of potato mixture.
Using a mister, lightly mist the potatoes with light olive oil, then bake for 10 minutes. Finish by broiling on high for about 5 minutes, or until the tops are golden brown. Keep a close eye while broiling to prevent burning: golden peaks can turn dark quickly. Garnish with chopped parsley before serving.