Chop strawberries and add them to a small sauce pot, heating over medium heat.
Add sugar, vanilla and lemon juice. Stir well.
Cover and cook for about 15 minutes, stirring often.
Use your immersion blender to puree strawberry mixture. (If you don't have an immersion blender, use a regular blender or a food processor.)
Set aside. (It should make a little more than 1/2 cup of strawberry sauce.)
To prepare pudding:
In a medium sauce pot, over medium heat, heat up milk, heavy cream and vanilla extract to 160 degrees. Stir well.
Combine flour and cornstarch in a medium mixing bowl, stir until all incorporated and set aside.
In a large metal mixing bowl, whisk egg yolks, salt and sugar.
Very slowly, while constantly stirring, pour ½ cup of milk mixture into the eggs.
Pour in another ½ cup of milk mixture, very slowly, keep whisking.
Slowly, whisk in dry ingredients.
Pour mixture from the mixing bowl back into the sauce pot, slowly whisking constantly. Whisk a little faster if you see any clumping while the mixture thickens.
Cook over medium heat, slow-stirring constantly, until mixture is thick (don't be concerned that mixture will look too thick because you will be adding strawberry sauce).
Remove from heat and add 1/2 cup of strawberry sauce. Whisk until completely combined. If the pudding still looks a little thick, add a little more strawberry sauce.
Let pudding cool to room temperature.
Transfer into a container with an air-tight lid and refrigerate until completely cold, at least 4 hours. (You can also use a bowl and saran wrap.)