Purée strawberries in a blender or food processor. Strain puréed strawberries through a sieve.
Transfer strawberry purée to a small saucepan. Stir in lemon juice.
Bring to a boil over medium heat. Reduce heat and simmer until strawberry purée is reduced by half.
Remove from heat. Stir in strawberry extract. Set aside to cool completey.
Strawberries and Cream Filling
Bring milk to a boil in a small saucepan over medium heat.
Meanwhile, whisk sugar, cornstarch and salt together in a medium bowl. Add the egg and whisk until smooth.
When milk starts to boil, remove from heat and pour 1/3 of the hot milk into the egg mixture and whisk to combine.
Pour the egg mixture back into the remaining hot milk and cook over medium heat, whisking continuously, until the mixture comes to a boil and thickens.
Remove from heat. Stir in butter and vanilla extract.
Pour mixture through a sieve placed over a bowl. Cover the surface with plastic wrap and let cool completely.
Set aside 2 tablespoons of strawberry purée. Add remaining strawberry purée to cooled pastry cream and stir to combine. Cover strawberry pastry cream and chill in refrigerator.
In a medium bowl, whip heavy cream to stiff peaks with an electric mixer at high speed. Fold whipped cream into cooled strawberry pastry cream. Set aside in refrigerator.
Preheat oven to 400ºF. Line 2 large baking sheets with parchment paper,
Combine water, butter and salt in a medium saucepan. Bring to a boil over medium heat.
Reduce heat. Add flour and stir vigorously with a wooden spoon until mixture pulls away from sides of pan and forms a ball.
Transfer mixture to the bowl of a stand mixer. Mix on low speed until steam dissipates and mixture cools to lukewarm.
Add eggs one at a time and beat on medium speed until smooth, stopping to scrape down bowl.
Transfer mixture to a piping bag fitted with a large round tip. (I used *Ateco tip 808)
Pipe 1 1/4-inch mounds, about 2 inches apart, on prepared baking sheets. Smooth tops with a wet finger.
Bake 15 minutes, then turn down the oven heat to 350ºF and continue baking until golden brown, about 8-10 more minutes. Using a toothpick or skewer, prick a small hole in each profiterole to allow steam to escape. Place on a wire rack to cool completely.
Use the tip of a paring knife to make a pilot hole in the bottom of each profiterole.
Place strawberries and cream filling into a piping bag fitted with a medium round piping tip. (I used **Wilton tip 12)
Place tip into the pilot holes and fill each profiterole with filling.
In a medium bowl, whisk all icing ingredients together until smooth. Spoon over filled profiteroles. Refrigerate profiteroles until ready to serve.