Add pasta to same pot of boiling water and cook, stirring occasionally, until al dente. Drain, reserving 1 cup pasta cooking liquid.
STEP 3
Heat oil in a wok or large skillet over medium. Cook mustard seeds until oil around seeds is sputtering (cover skillet if you are getting spattered), about 10 seconds. Add curry leaves, urad dal, and asafetida and stir to combine. Cook until fragrant and urad dal is golden, about 1 minute.
STEP 4
Add corn (and fresh or frozen pea and/or green beans if using) to wok and cook, stirring occasionally, until tender, about 2 minutes. Add pasta and toss to combine, then add butter, 2 oz. Parmesan, and reserved pasta cooking liquid and toss until butter and cheese are melted and coat pasta. Add chana dal and toss again to combine.