Peel and chop the potatoes. Place them in a medium saucepan and cover them with cold water. Place the saucepan over medium-high heat and bring to a boil. Lower the heat to a simmer and cook the potatoes for 12 minutes, or until quite mushy and soft. Drain the potatoes and return them to the pot to dry out for a minute or so.
Place the potatoes in a large bowl and set aside.
Fill the same medium saucepan with 3 ¼ cups of water. Bring the water to a boil over medium-high heat. Add the split peas and stir. Lower the heat to a simmer. Cook until the split peas have absorbed most of the liquid and are quite soft/mushy, about 35 minutes.
Take the split peas off the heat and mash them with a fork. Transfer the mashed split peas to the bowl with the potatoes.
Add the grated carrots to the bowl, along with the onion, garlic, cumin, coriander, turmeric, fenugreek (if using), chickpea flour, lemon juice, and tamari. Season everything liberally with salt and pepper. Taste the mixture and adjust seasoning if necessary.
Mix and mash all of the ingredients together with your hands. This part is messy! It should feel very pasty when you’re done with it, with only a few tiny pieces of whole potato in the mix.
Form the mixture into 10 split pea patties and place them on a baking sheet. Cover the baking sheet with plastic wrap and slide into the refrigerator for at least 2 hours.
Once you’re ready to cook the patties, heat a decent slick of oil in a large skillet over medium-high heat. Set your oven to 300 degrees F, and place a large baking sheet inside.
Cook the patties in batches, browning the sides thoroughly. Each side should take about 2 full minutes. As you finish cooking the patties, transfer them to the baking sheet in the oven while you cook those that remain. Once you're done cooking all of the patties, it's advantageous to leave the patties in the oven for a good 10 minutes so that they can firm up even more so.
Serve the split pea patties hot with lettuce wraps, rolls, a salad, or any other accompaniment you like.