Peel 1 onion and chop. Smash 6 garlic cloves with the flat side of your knife. Peel, then finely chop. Peel 3" piece ginger with a small spoon, then finely chop.
Heat 2 Tbsp. oil in large Dutch oven over medium. Add onion and cook, stirring often, just until translucent, 6–8 minutes.
Add garlic and ginger and cook, stirring often, until garlic is starting to turn golden, about 5 minutes.
Add 5 tsp. curry powder and ½ tsp. cayenne and cook, stirring constantly, until spices are aromatic and starting to stick to bottom of pot, about 1 minute.
Add 13.5 oz. coconut milk and stir to loosen spices, then stir in 1 cup lentils, ½ cup shredded coconut, 2 tsp. salt, and 5 cups water.
Bring to a boil over medium-high heat, then reduce heat to medium-low to keep soup at a gentle simmer. Cook, stirring occasionally, until lentils are broken down and soup is thickened, 25–30 minutes.
Meanwhile, remove 10 oz. thawed frozen spinach from packaging and squeeze between your hands over sink to remove excess water. Transfer to cutting board and coarsely chop.
Add spinach and 15 oz. tomatoes to pot and stir to combine. Taste and season with more salt. Simmer just to let flavors meld, about 5 minutes. Taste and season again with more salt.