Step 1

Combine 1 large russet potato (about 10 oz.), peeled, cut into 1" pieces, 1 small carrot, peeled, sliced crosswise ½" thick, 2 cups frozen cauliflower florets, ½ cup frozen green peas, 2 Tbsp. unsalted butter, and 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt in a medium saucepan. Pour in 1 cup water and bring to a simmer. Reduce heat to medium-low, cover, and cook until potato is falling apart and carrot and cauliflower are tender, 12–18 minutes. Remove from heat and mash with a potato masher or fork until mostly smooth, but not quite a purée. Cover and keep warm.

Step 2

Set aside ½ cup finely chopped red onions (from 2 large red onions, finely chopped) for serving. Heat 2 Tbsp. vegetable oil in a medium Dutch oven or other heavy pot over medium-high. Cook 2 tsp. cumin seeds until fragrant and a shade darker, about 45 seconds. Add remaining red onions to pot along with 1 medium green bell pepper, ribs and seeds removed, finely chopped, one 2" piece ginger, peeled, finely chopped, 8 garlic cloves, finely chopped, and remaining 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt. Cook, stirring occasionally, until onions are translucent and golden brown in spots, 10–15 minutes. Reduce heat to medium and add 2 Tbsp. unsalted butter, 3 Tbsp. double-concentrated tomato paste, 1 Tbsp. plus 1 tsp. ground coriander, 1 Tbsp. ground cumin, 1 Tbsp. sweet paprika, 1 tsp. cayenne pepper, ½ tsp. ground turmeric, and ¼ cup water. Cook, stirring often to ensure spices don’t stick and burn, until mixture is slightly darkened, 6–8 minutes. Pour in another ¼ cup water and cook, stirring often, until oil beads on surface of aromatics, about 5 minutes.

Step 3

Scrape mashed vegetables into pot with aromatics; add 1 tsp. garam masala and 1 cup water. Cook, stirring occasionally and adding a splash of water if needed, until mixture is homogeneous and slightly thickened (texture should be loose, similar to risotto), 10–15 minutes. Remove from heat and stir in 3 Tbsp. unsalted butter and 2 Tbsp. fresh lime juice. Taste and add more salt if needed. Transfer bhaji to a large shallow bowl and top with a few pats of butter, reserved red onions, and ½ cup finely chopped cilantro.

Step 4

Heat 1 Tbsp. unsalted butter in a large skillet, preferably cast iron, over medium. Working in batches and adding more butter between batches if pan looks dry, toast 6–8 potato rolls, cut side down, until golden brown, about 2 minutes.

Step 5

Serve bhaji with potato rolls and lime wedges alongside.