Position a rack in the center of the oven; preheat to 350°F. Line 2 baking sheets with parchment. Set a wire rack over a parchment-lined tray for glazing later. Sift the powdered sugar for the glaze and set it aside.
Whisk the oil, egg, and egg yolk in a large bowl until glossy. Add the cake mix and salt; fold with a spatula just until no dry streaks remain. The dough will be thick. Let it rest 10 minutes to firm up.
Scoop 1 1/2-tablespoon portions of dough onto the prepared sheets, spacing about 2 inches apart (24 cookies total). Lightly flatten each mound to about 1/2 inch thick with damp fingers for even baking.
Bake one sheet at a time for 8–10 minutes, until the edges look set and the centers are slightly puffed but soft. Cool on the sheet for 3 minutes, then transfer cookies to the wire rack. Repeat with the second sheet.
While the first tray bakes, make the glaze: In a small saucepan over medium-low heat, melt the butter with the evaporated milk until steaming. Whisk in the cocoa and let it gently bubble for 15–20 seconds to bloom the cocoa.
Remove from heat; whisk in vanilla, then gradually whisk in the sifted powdered sugar until smooth and pourable. If the glaze seems too thick, whisk in 1–2 teaspoons more evaporated milk. Keep warm on the lowest heat, stirring occasionally.
While cookies are just barely warm, spoon a generous tablespoon of warm glaze over each cookie, nudging it to the edges so it gently cascades down the sides. Tap the rack to help the glaze settle into a smooth finish.
Let the glaze set until matte and sliceable, 20–30 minutes. Store cooled cookies in an airtight container at room temperature for up to 3 days.