Adjust oven rack to middle position and heat oven to 300 degrees. Grease and flour 12-cup Bundt pan.
Combine flour and salt in bowl. Whisk eggs and yolks, milk and vanilla together in a 2 cup liquid measuring cup.
Using stand mixer fitted with paddle, beat sugar, butter and cream cheese on medium-high speed until pale and fluffy, about 3 minutes. Reduce speed to low and very slowly add egg mixture until incorporated (batter may be slightly curdled).
Add flour mixture in 3 additions, scraping down bowl as needed. Give batter final stir by hand.
Scrape batter into prepared pan and gently tap pan on counter to release air bubbles. Bake until toothpick inserted in center comes out clean, 80 to 90 minutes, rotating pan halfway through baking.
Cool cake pan on wire rack for 15 minutes. Remove cake from pan and cool completely, about 2 hours. Serve.
Cake can be wrapped in plastic wrap and held at room temperature for 3 days.