Step 1

Place a rack in middle of oven; preheat to 350°. Set a 9x5" loaf pan inside a 13x9" baking dish. Bring 1 cup (200 g) sugar, 1 Tbsp. light corn syrup, and 3 Tbsp. water to a boil in a small saucepan over medium heat, swirling pan occasionally (do not stir). Cook until caramel is dark amber, about 4 minutes. Carefully pour into loaf pan and let sit until set, about 10 minutes.

Step 2

Using an electric mixer on medium speed, beat 8 oz. cream cheese, room temperature, and ½ cup (100 g) sugar in a medium bowl until combined. Beat in 4 large egg yolks and 3 large eggs; scrape down sides of bowl. Scrape in vanilla seeds from 2 vanilla beans; reserve pods for another use. Reduce mixer speed to low, add one 14-oz. can sweetened condensed milk, one 12-oz. can evaporated milk, and 1 cup whole milk, and beat until custard is smooth, about 1 minute.

Step 3

Pour custard into loaf pan. Pour water into baking dish to come ¾" up sides of loaf pan. Bake flan until pale golden on top and just set in the center but still a little wobbly when jiggled, about 1½ hours. Remove loaf pan from baking dish and transfer to a wire rack. Let flan cool in pan 15 minutes, then chill at least 3 hours and, preferably, up to 12 hours.

Step 4

Just before serving, run a small knife around edges of flan. Set a platter on top of loaf pan and carefully invert flan onto platter.