Begin by preparing the potatoes. In a large pot, add the 2 cups of broth, 4 cups of water, a generous pinch of salt and bring to a boil. Once boiling, add potatoes (add extra water to cover them if needed), reduce to a simmer, and cook for 25-30 minutes until tender and can easily be pierced with a fork.
While the potatoes are cooking, prepare the filling. In a large and deep skillet or pot on medium-high heat, warm the olive oil. Add onions and carrots and cook for 5-7 minutes until tender and onions are translucent.
Add mushrooms, stir to combine with the onions and carrots, and cook for an additional 3-4 minutes until mushrooms have reduced in size by roughly half. Add garlic and thyme, stir to combine with the vegetables, and cook for an additional minute until fragrant.
Reduce heat to low-medium, add dry lentils, stir to combine with the vegetable mixture. Add flour, tomato paste, and Worcestershire sauce, and stir until everything is well combined.
Add broth and salt, stir again until everything is well incorporated, increase heat to bring to a boil, and then cover and reduce to a simmer and cook for 35-40 minutes or until all of the water is absorbed and lentils are tender.
Once the potatoes are tender, drain them in a colander and then return them to the pot. Add butter, a splash of milk, and a generous pinch of salt, and mash until well fluffy, adding more butter and/or milk as needed. Once mashed, taste and season with additional salt and pepper as needed.
Preheat the oven to 400°F.
Once the lentils are cooked, add peas and stir to combine with the lentil mixture. Taste and add additional salt and pepper as needed. Then remove from the heat and set aside.
Once the filling is ready and the potatoes are mashed, transfer the lentil mixture to a large baking dish, spreading it out evenly. Dollop the mashed potatoes on top of the filling and spread it to cover the lentil mixture, right to the edges to ensure the mixture doesn’t bubble out of the dish, until well covered.
Transfer the baking dish to the oven to bake for 25-30 minutes until bubbling and golden brown. You can place a baking sheet underneath it to prevent spillage.
Once baked, remove the baking dish from the oven and allow it to cool for 10 minutes before serving.
Any leftovers can be stored in airtight containers in the fridge for up to 5 days or in the freezer for 3 months.