Bring a large pot of water to a boil. Add 1 teaspoon of salt per quart of water, then add the green beans. Cook for about 4 minutes, until crisp-tender. Immediately transfer the beans to ice water. Once cool, drain thoroughly and pat dry.
Heat a large, dry skillet over medium-low heat. Add the chopped pistachios and toast for 3–5 minutes, stirring frequently, until fragrant and lightly golden.
Stir in the cumin, cinnamon, and red pepper flakes during the last 30 seconds of toasting. Remove the skillet from the heat, stir in the everything bagel seasoning, and transfer the pistachio mixture to a bowl.
In the same skillet, melt the butter over medium heat, stirring frequently, until the milk solids turn golden brown and smell nutty. Reduce the heat to low.
Add the dried green beans to the brown butter and sauté for 5–6 minutes, until heated through. Stir in three-quarters of the pistachio mixture near the end of cooking. Remove the skillet from the heat and taste before adding any additional salt.
In a small food processor, blend the feta, Greek yogurt, lemon juice, olive oil, and garlic until smooth and creamy, scraping down the sides as needed.
Spread the whipped feta in a thin layer over a serving platter. Top with the green beans, spooning over any brown butter and pistachios from the skillet. Finish with the reserved pistachio mixture, pomegranate seeds, and fresh lemon zest.