Place a medium-sized heat proof bowl with a fine mesh strainer near the stove.
Remove the stems from the strawberries. Coarsely chop the strawberries and place them in a 4-quart saucepan with the sugar and lemon juice. Bring the strawberries to a boil and then reduce to medium heat. Cook the berries, stirring occasionally until they're reduced to 1-3/4 cups. About 7 minutes.
If there are any pieces of strawberry left smash the strawberries or use an immersion blender to completely puree them. Taste the strawberries and add more sugar if you want it a little sweeter. Add additional sugar 2 tablespoons at a time until the desired level of sweetness is achieved, but be careful not too add too much as the curd is supposed to be a little tart.
Cool the mixture to room temperature. Add the whole eggs, and egg yolks and salt. Whisk to combine the eggs and strawberries.
Cook over medium heat, whisking constantly until it starts to thicken and reaches about 190 degree F, about 10-12 minutes. The final mixture will not be as thick as a traditional lemon curd, but will thicken a little more after it is refrigerated.
Remove the pot from the heat, and add the butter one tablespoon at a time, whisking after each addition until the butter is thoroughly combined. Strain the curd into a bowl to remove the solids.
Cover with plastic wrap by lightly pressing the plastic wrap onto the surface of the strawberry curd to keep a skin from forming as it cools. Place the curd in the refrigerator to cool for at least 4 hours, preferably overnight. The curd will thicken as it cools.
The curd is good for up to 3 weeks in the refrigerator.