Place 3 Tbsp. cold water in a small shallow bowl and sprinkle 2 tsp. unflavored powdered gelatin evenly over (do not stir). Let sit until gelatin is softened, 5–10 minutes.
Vigorously whisk 4 large egg yolks and ¾ cup (150 g) granulated sugar in a small saucepan, making sure no unincorporated sugar is trapped around sides of pan, until combined and mixture is pale and thick, about 2 minutes. Whisking constantly and scraping sides of pan often, stream in ½ cup fresh orange juice and ¼ cup fresh lemon juice; whisk until mixture is smooth. Add 1 tsp. ground cardamom and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt and whisk just to combine.
Place saucepan over medium-low heat and cook mixture, whisking constantly, until foaming subsides and curd barely holds marks from whisk and is thick enough to coat a spoon, about 5 minutes (if you want to be really precise, an instant-read thermometer should register 170°). Immediately remove saucepan from heat and scrape in softened gelatin (it will have solidified). Whisk briskly to dissolve and incorporate gelatin into curd, about 30 seconds.
Add 1 lb. frozen mango chunks (about 4 cups) to curd and stir to combine. Let sit until mango is mostly thawed and curd is cold, about 5 minutes. Using an immersion blender, blend mango into curd until combined and smooth. (Alternatively, you can use a standard blender and blend on high.) Measure out 1 cup mango curd; set aside. Add ½ cup plain whole-milk Greek yogurt to remaining mango curd in saucepan and whisk until incorporated and smooth.
Using an electric mixer, beat 2 cups chilled heavy cream in a large bowl, starting on low and gradually increasing speed to medium-high as it thickens, until stiff peaks form. Scrape curd mixture into bowl and gently fold with a rubber spatula until only a few streaks of whipped cream remain.
Divide mousse among 8 glasses. Tap each glass gently on the counter to help mousse settle, then top each with about 2 Tbsp. reserved mango curd. Cover and chill until cold and set, at least 4 hours.
Do ahead: Mousse can be assembled 3 days ahead. Keep chilled until ready to serve.