Step 1
Wrap one 10-oz. package frozen chopped spinach, thawed, in a clean kitchen towel and twist and squeeze towel tightly over the sink to expel as much liquid as possible.
Step 2
Melt 2 Tbsp. unsalted butter in a medium Dutch oven or other heavy pot over medium-high heat. Add spinach and ½ cup finely chopped herbs (such as cilantro, parsley, and/or dill) and season with kosher salt. Cook, stirring occasionally and breaking up spinach, until mixture is combined and spinach and herbs are slightly darkened in color, about 4 minutes. Transfer to a bowl.
Step 3
Heat 3 Tbsp. extra-virgin olive oil in same pot over medium-high. Add 3 medium onions, thinly sliced, and season with salt. Cook, stirring occasionally, until lightly browned and frizzled around the edges, 9–12 minutes. Add 5 garlic cloves, thinly sliced, and cook, stirring often, until softened and fragrant, about 1 minute. Add 1 Tbsp. ground coriander, 2 tsp. ground cumin, ½ tsp. crushed red pepper flakes, and a few grinds of freshly ground black pepper. Cook, stirring often, until combined, about 1 minute.
Step 4
Add ⅔ cup basmati rice, ⅔ cup French green lentils, 4 cups low-sodium vegetable broth, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, and 6 cups water; stir to combine. Increase heat to high and bring soup to a boil. Reduce heat so soup is at a simmer and cook until rice is cooked through and lentils are tender (they will still retain a bit of bite), 30–35 minutes.
Step 5
Stir spinach mixture into soup and cook, stirring often, until combined and heated through, about 3 minutes. Remove pot from heat and add juice of 1 lemon and remaining 2 Tbsp. unsalted butter; stir until butter is melted. Taste soup and season with salt and black pepper.
Step 6
Mix 1 cup plain whole-milk yogurt, a big pinch of salt, and remaining 2 Tbsp. extra-virgin olive oil in a small bowl to combine. Ladle soup into bowls and top each with a spoonful of yogurt mixture to serve.