Combine olive oil, lemon juice, Dijon mustard, and minced garlic in a bowl.
Whisk vigorously for 30-45 seconds until the mixture emulsifies and becomes slightly thickened.
Season with sea salt and black pepper, whisking to incorporate.
If desired, stir in grated Parmesan cheese for extra richness and depth of flavor.
Taste and adjust seasoning or acidity as needed. Add more olive oil if too tangy or more lemon juice if you want more brightness.
Transfer to an airtight glass jar and store in the refrigerator for up to one week.