Preheat your oven to 300°F (150°C). Prepare your square tube pan by fitting a square of parchment paper between the two pieces of the pan and brushing with pan coat or baking spray.
In the bowl of a stand mixer, beat the butter and sugar together until pale, light, and fluffy — about 5 minutes.
Add ½ cup of flour, the cream cheese, salt, and vanilla extract. Beat until everything is combined and smooth.
Scrape the bottom and sides of the mixing bowl to ensure even mixing.
With the mixer running at low speed, add 1 egg at a time, beating for 30 seconds after each addition. Repeat with all 10 eggs.
Gradually add the remaining flour in 2 parts, mixing on low until the flour just disappears. Scrape the bowl and mix for another 15 seconds to fully incorporate.
2️⃣ Bake the Cake:
Pour the batter into the prepared tube pan and gently shake the pan to settle the batter.
Place the pan on the middle rack of the oven, with a baking sheet on the rack below it to catch any drips.
Bake for 2½ hours, or until a skewer inserted into the cake comes out clean.
Let the cake cool in the pan for 15 minutes. To unmold, place the pan over a metal can (like one that contains beans or tomatoes) and push down to remove the outer piece.
Once the cake is cool enough to handle, lift it or turn it out onto a wire rack to cool completely.
3️⃣ Prepare the Caramel Glaze:
In a medium saucepan over medium-low heat, combine sweetened condensed milk, sugar, and butter. Stir occasionally and cook until the mixture reaches 235° to 240°F (you can also cook for about 8 minutes after bubbles begin to break on the surface, if you don’t have a thermometer).
Remove from heat and let the glaze cool until it thickens slightly.
