Heat oil in a medium nonstick ovenproof or cast-iron skillet over medium-high heat. Add squash and cook, stirring occasionally, until just fork-tender, about 10 minutes. Add shallot; cook for 1 minute. Stir in kale by the handful. Add water; cover and reduce heat to medium-low. Cook until the kale is tender, about 5 minutes. Remove from heat; spread the mixture evenly in the pan.