In a medium pot, add the lentils and enough water to cover by 2-inches. Bring the water to a boil, then reduce the heat to low and simmer for 15-20 minutes, or until the lentils are tender, but not mushy. Depending on how fresh/old your lentils are, they will cook a lot faster or slower, so keep an eye on them and taste as you go. Drain the lentils and return them to the pot. Stir in the mustard, oil, vinegar, and salt until well combined.
Preheat the oven to 425F.
Cut the leeks in half lengthwise (watch video). Rinse them under water to remove any dirt in all of those layers. We are eating the whole leek, so don’t trim off the tops!
In a 9x13-inch baking dish, add the leeks, carrots, olive oil, and salt and toss to coat thoroughly. Spread everything out into an even layer, placing the leeks cut-side-down. Bake for 20 minutes.
Add water and peas to the baking dish, cover tightly with foil, and bake for 10 more minutes. Your leeks should be very soft and carrots fork tender.
Remove the leeks and carrots and use a sharp knife to cut them into more manageable, bite-sized pieces, then return to the baking dish.
Serve the leeks/carrots/peas over a bed of the warm lentils. Top with plenty of feta cheese, an egg (if using), a generous drizzle of your best olive oil, nuts, herbs, black pepper, and a generous squeeze of lemon.