Prepare the strawberries. If using frozen, thaw and gently cook them until soft enough to blend. If using fresh, wash and remove the stems.
1 cup strawberry puree
Make the puree. Blend the strawberries until smooth, then strain through a fine-mesh sieve. Set aside to cool — do not add hot puree to the egg yolks.
Heat the milk. Combine the milk, sugar, and vanilla extract in a saucepan. Heat over medium, stirring occasionally, until it just begins to steam and is close to a boil.
1 cup milk, 7 tbsp sugar, 1 tsp vanilla extract
Prepare the yolk mixture. While the milk heats, whisk together the egg yolks, strawberry puree, and cornstarch in a large heatproof bowl until smooth and no lumps remain.
4 egg yolks, 5 tbsp cornstarch
Temper the eggs. Remove the milk from the heat. Slowly pour it into the yolk mixture in a thin, steady stream, whisking constantly. Don't rush this step — adding the hot milk too fast can scramble the yolks.
Cook until thick. Pour the mixture back into the saucepan. Cook over medium heat, whisking constantly, until it thickens and begins to bubble. Once bubbling, reduce the heat and whisk for another 30–60 seconds to cook out the raw starch taste.
Whisk off heat. Remove from the heat and continue whisking for 30–60 seconds. This loosens the cream slightly so it sets smooth rather than stiff.
Add the butter. Stir in the butter until fully melted and incorporated.
2 tbsp unsalted butter
Taste and adjust. Add lemon juice, extra sugar, or a pinch of salt to taste.
1 tbsp lemon juice
Strain if needed. If the cream isn't as smooth as you'd like, pass it through a fine-mesh sieve.
Cool. Transfer to a bowl and press plastic wrap directly onto the surface to prevent a skin from forming. Cool slightly at room temperature, then refrigerate until fully chilled.