Place the carrots in a single layer on a baking sheet, drizzle with 2 tablespoons of oil and season with 1 teaspoon of salt and ½ teaspoon of pepper. Roast the carrots until tender and starting to caramelize, about 30 – 40 minutes. Let cool slightly. Leave oven on.
While the carrots are roasting, combine the lentils, the smoky flavor packet, and 4 cups water in a saucepan. Bring to a boil, lower the heat and simmer, covered, for 30 – 35 minutes or until the lentils are tender. Drain off any leftover water.
Heat 2 tablespoons of olive oil in a large skillet. Add the chopped onions and cook for 5 minutes over medium-high heat or until softened. Add the garlic and cook for 30 seconds.
Place half the onion and garlic in a food processor along with half the cooked lentils, the Vegenaise, 1 teaspoon of salt and ½ teaspoon of pepper and process until smooth. Add the remaining lentils and pulse a few times. You want some texture to the cakes.
Line a baking sheet with parchment paper and scoop out the lentil mixture with a 1/3 measuring cup, form into patties and place on the prepared baking sheet. Spray lightly with cooking spray and bake for 20 minutes or until firm to the touch.
Clean out the food processor bowl, add the carrots, the remaining onions and garlic, smoked paprika, vinegar and almonds. Process until it has a meal-like texture, scraping down the sides of the bowl a few times. Add 4 tablespoons of olive oil and puree. If the mixture is too thick, add another tablespoon or two of oil and puree. Taste and season with more salt and pepper if desired.
Serve the lentil cakes topped with the Romesco sauce.