Heat 3 Tbsp. extra-virgin olive oil in large skillet, preferably cast iron, over medium. Cook 1 medium onion, cut into ¼" pieces, 6 garlic cloves, thinly sliced, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, stirring occasionally, until onion is softened and translucent, 6–8 minutes. Add 2 Tbsp. all-purpose flour and 2 tsp. freshly ground pepper and cook, stirring often, until flour is lightly toasted (it will start to stick to bottom of pan), about 2 minutes.

Pour 1½ cups water into skillet, then add 4 oz. cream cheese, cut into 1" pieces, 2 Tbsp. white or yellow miso, and 1 Tbsp. chicken or vegetable bouillon paste. Cook, stirring often with a whisk or heatproof rubber spatula, until cream cheese is melted and miso and bouillon paste are dissolved, about 3 minutes. Continue cooking sauce, stirring.

Add two 15.5-oz. cans chickpeas, rinsed, and two 10-oz. packages frozen broccoli florets or cuts, coarsely chopped if large; cook, stirring occasionally, until broccoli is thawed and sauce is clinging to chickpeas, 6–10 minutes. Add 2 oz. Parmesan, finely grated, and stir until melted and incorporated. Taste chickpea mixture and season with more salt if needed.

Heat broiler. Generously top chickpea mixture with more Parmesan and broil until cheese is melted and golden in spots, 6–10 minutes.

Serve chickpeas and broccoli with country-style bread for swiping through sauce if desired.