Tear kale leaves from stems, keeping leaves as intact as possible. Stack leaves, roll into rough bundles, and slice into thin (1/4 in.) ribbons.
Heat oil in a large wide pot over medium-low heat. Add shallots and cook, stirring, until just beginning to brown, 3 to 5 minutes.
Add kale ribbons and salt. Cook over medium-high heat, turning often with tongs, until kale is just wilted but still bright green, 4 to 7 minutes (if you're cooking it to store, keep it slightly crunchy, since it will soften when you reheat). Serve warm or at room temperature.