Make the custard: Heat oven to 350°. Lightly oil the inner sides of a 10" springform pan and tightly wrap bottom and sides with aluminum foil. Melt ½ cup sugar in a 2-qt. saucepan over medium-high heat. Cook, without stirring, until sugar is a deep golden brown, 12–13 minutes. Carefully pour caramel into springform pan; tilt pan to evenly distribute caramel over the bottom and place pan inside a roasting pan. Whisk remaining sugar with egg and yolks until thick. Whisk in milk, condensed milk, and passion fruit concentrate to make a smooth custard. Pour custard over caramel; transfer roasting pan to oven. Pour boiling water into roasting pan to come halfway up outside of springform pan. Bake until custard is set but still slightly loose in center, about 1 hour. Transfer springform pan to a wire rack; let cool. Chill at least 2 hours or up to overnight.
Make the syrup: Boil sugar and ¼ cup water in a 1-qt. saucepan; cook, stirring occasionally, until sugar is dissolved and syrup is thick, about 10 minutes. Whisk in passion fruit seeds and pulp; cook until pulp has dissolved in syrup, 3–4 minutes more; let cool completely.
To serve: Unmold and invert custard onto a serving platter. Slice into wedges and drizzle with passion fruit syrup.