Toss the diced zucchini with the half teaspoon of salt in a colander and let it drain 15 minutes. Pat it aggressively dry. This step is the recipe.
Heat the oil in a wide skillet over medium-high. Cook the onion 3 minutes, then the garlic and jalapeno for 1 more.
Add the dried zucchini in as close to one layer as fits. Cook 4 to 5 minutes, stirring only twice, so it browns in spots instead of steaming.
Add the tomato, corn, cumin and oregano. Cook 3 to 4 minutes until the tomato softens but the zucchini still has bite.
Kill the heat, scatter the cheese over, and lid the pan 2 minutes to melt.
Finish with cilantro, taste for salt, and serve from the skillet.