Combine lemon zest and sugar in a blender or food processor; pulse until zest is finely minced.
Add butter and blend.
Add eggs, lemon juice, lemon extract, and salt; blend until combined.
Pour mixture into medium saucepan and cook over medium-low heat, stirring occasionally, until thickened (just below simmer - 170 degrees F).
Continue stirring 2-3 minutes after mixture thickens.
Remove from heat and transfer to a wide mouth glass jar with a lid.
Place in refrigerator to cool.
Keep refrigerated.