For the crust: Preheat oven to 350°. Mix crushed biscuits and sugar together in a medium bowl. Add butter and stir until well combined. Transfer crumb mixture to a 10" false-bottom tart pan. Using your hands, spread mixture out in an even layer, then use your fingertips to press crumb mixture into bottom and up side of pan to form an even crust. Transfer to a baking sheet and bake until crust is set and lightly golden in places, about 15 minutes. Set crust aside until completely cool.
For the filling: Melt chocolate in a medium heatproof bowl set over a medium pot of gently simmering water over medium-low heat, stirring constantly, about 5 minutes. Remove bowl from heat and set aside. Heat cream in a medium saucepan over medium heat until bubbles appear around inside edge of pan and cream is just about to boil, then remove pan from heat. Meanwhile, put egg yolks into a medium mixing bowl and whisk until smooth. Gradually whisk about 1⁄4 cup of the hot cream into yolks, then stir egg–cream mixture back into pot of hot cream. Gradually add egg–cream mixture to bowl of melted chocolate, stirring until well combined and smooth.
Pour filling into prepared crust and set aside to cool, about 30 minutes, then refrigerate until chocolate is completely set, about 3 hours. Remove outer ring of tart pan. Serve with sliced strawberries, if you like.