► Set a fine-mesh strainer over a medium bowl and set bowl in an ice bath.
► Combine milk, sugar, and salt in a small saucepan and simmer over medium heat until sugar has completely dissolved. Remove pot from heat. Whisk together egg yolks in a small bowl. Whisk a small amount of warmed milk into yolk mixture. Whisking constantly, add a bit more warm milk to yolks. Add yolk mixture to pot with remaining milk.
► Gently cook mixture over medium-low heat, stirring constantly with a wooden spoon or silicone spatula, until mixture thickens and coats back of spoon. Strain custard into prepared bowl and stir to cool slightly, 10 to 15 minutes. Remove bowl from ice bath and refrigerate uncovered until custard has completely chilled, at least 2 hours.
► Once chilled, stir in crème fraîche, preserved lemon juice, and vanilla. Churn in an ice cream machine according to manufacturer’s instructions. Five minutes before ice cream is done, add preserved lemon pulp, a little at a time so it distributes evenly. Serve immediately for a soft-serve texture, or transfer to a freezer-safe container, cover, and freeze for a few hours to harden.
► To serve, top each bowl with a drizzle of olive oil and a pinch of sea salt.