Whisk the eggs, then stir in the canned pineapple with its juice, vegetable oil, and vanilla until combined.

In a separate bowl, whisk the flour, sugar, baking soda, and salt until evenly mixed.

Add the dry ingredients to the wet in two additions, stirring just until no flour streaks remain. Pour into a greased and floured 10-cup bundt pan. Bake at 350°F (175°C) for 45-50 minutes, until a toothpick comes out with a few moist crumbs. Cool in the pan for 10 minutes, then invert onto a rack to cool completely.

Beat the cream cheese, powdered sugar, vanilla, and 2 tbsp milk until smooth. Add more milk if needed for a thick, pourable glaze. Spoon over the completely cooled cake and serve.