Melt butter with oil in a large skillet over medium heat. Add onion; cook, stirring occasionally, until starting to soften, 3 to 4 minutes. Add anchovies and turmeric; cook, stirring often, until anchovies dissolve, 2 to 3 minutes. Add couscous; cook, stirring occasionally, for 3 minutes.
Add broth, salt, and pepper. Increase heat to high; bring to a boil. Cover and reduce heat to medium-low. Simmer until liquid is nearly absorbed, about 12 minutes. Stir in zucchini and spinach. Cover and cook until spinach is wilted and zucchini begins to soften, 2 to 3 minutes. Remove from heat and sprinkle with cilantro.