Heat 1 Tbsp. vegetable oil in a large Dutch oven or other heavy pot over medium-high. Add ½ lb. mixed mushrooms (such as crimini, button, oyster, beech, and/or shimeji), cut into 2" pieces, arranging in a single layer, and season with kosher salt. Cook, undisturbed, until golden brown underneath, about 4 minutes. Turn mushrooms over and cook until browned on other side, about 4 minutes; transfer to a plate. Add 1 Tbsp. vegetable oil to pot and repeat process with remaining ½ lb. mixed mushrooms.

Heat remaining 3 Tbsp. vegetable oil in same pot (do not wipe out) over medium. Add 1 dried bay leaf and 1 tsp. cumin seeds; cook, stirring, until fragrant, about 1 minute. Add 1 large onion, finely chopped, ½ jalapeño, finely chopped, 3 garlic cloves, finely grated, and one 1" piece ginger, peeled, finely grated; stir to combine. Cook, stirring occasionally, until onion is translucent and golden brown around edges, 15–20 minutes. Add 1 Tbsp. plus 1 tsp. ground coriander, 1 tsp. garam masala, 1 tsp. Kashmiri chile powder or paprika, ½ tsp. cayenne pepper, and ½ tsp. ground turmeric; cook, stirring often, until spices are fragrant, about 3 minutes. Add 3 Tbsp. double-concentrated tomato paste; cook, stirring constantly, until paste is slightly darkened in color, about 3 minutes. Pour in 1½ cups water and bring to a simmer, stirring and scraping up browned bits with a wooden spoon.

Return mushrooms and any accumulated juices to pot, then stir in 8 oz. green beans, trimmed, halved crosswise, ½ cup heavy cream, and 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt. Partially cover pot and bring to a simmer. Cook, stirring occasionally, until green beans are tender and sauce is thickened, 15–20 minutes. Remove from heat; discard bay leaf. Stir in 1 Tbsp. fresh lime juice and remaining 3 Tbsp. heavy cream.

Serve with steamed rice and lime wedges.