Preheat the oven to 425°F. Line a baking sheet with parchment paper and set aside.
Pour the milk and walnuts into a small saucepan and bring to a low boil. Remove the pan from the heat and cover. Leave the nuts to steep for 1 hour.
While the nuts are steeping, cut the cabbage lengthwise into 1-inch slices, keeping the core intact. Arrange the cabbage slices on the baking sheet and drizzle with the olive oil. Sprinkle with 1 teaspoon of the salt followed by the crushed red peppers flakes.
Place the baking sheet in the oven and roast for 25-35 minutes or until the edges are charred and the cabbage is tender. Set aside.
Pour the milk and walnut mixture through a fine mesh strainer. Reserve the milk and transfer the walnuts to a large food processor. Add the tahini, the juice of 1 lemon, the garlic, and the remaining salt. Blitz until a smooth paste forms. Set the food processor to low and stream in the sesame oil. Transfer the mixture to a bowl and set aside.
Heat a quarter-sized amount of olive oil in a large, deep skillet. Add the onion and a pinch of salt and saute until just translucent, about 3-5 minutes. Add the chickpeas and the water and bring to a boil. Reduce to a simmer and let cook for 10 minutes or until the chickpeas are tender and the water is almost entirely absorbed.
While the chickpeas are cooking, put a large pot of water on to boil. Add salt and the tagliatelle and cook according to the package's directions. Drain the cooked pasta and reserve a little of the cooking water for later.
Add the walnut paste to the chickpeas and onion and saute until the oils begin to release - about 2-3 minutes. Stir in the reserved milk and bring to a low boil. Reduce to a simmer and cook until thickened - about 5 minutes.
Remove the core from the roasted cabbage and add the remaining ribbons to the pan. Cook until the cabbage is heated through.
Take the skillet off of the heat and stir in the yogurt and the juice of the remaining lemon. Taste and season with salt accordingly. Add the pasta to the skillet and toss to coat. Use as much of the reserved pasta water as is needed to form a silky smooth sauce.
Transfer the pasta to a large serving platter and top with feta cheese, fresh parsley, and pomegranate arils. Serve immediately.