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Bring a large pot of well-salted water to a boil over high heat.
Heat the olive oil in a 12-inch skillet over medium-high heat. When the oil is hot, add the onion and a large pinch of salt and cook, stirring frequently, until the onion is beginning to soften and brown, about 5 minutes. Lower the heat to medium and continue cooking, stirring frequently, until the onion is very soft and light golden brown, about 15 minutes more (if the onion begins to look like it's burning, add 2 Tbs. warm water and lower the heat).
Put the orecchiette in the boiling water and cook until just shy of al dente, about 9 minutes. Add the green beans to the pasta water in the last minute of cooking.
While the pasta cooks, add the corn, jalapeño, and a pinch of salt to the onion and cook, stirring occasionally, until the corn kernels begin to soften, 3 to 5 minutes. Remove from the heat.
Reserve 1/2 cup of the pasta and green bean cooking water and drain the pasta and green beans together in a colander.
Return the orecchiette, green beans, and 2 Tbs. of the reserved water to the pot. Add the onion mixture and toss over medium heat until the green beans are crisp-tender and the orecchiette is perfectly al dente, 1 to 2 minutes. Add more of the pasta water as necessary to keep the dish moist. Season to taste with salt and pepper, transfer to warm shallow bowls, and top each serving with the pecorino and parsley.