Emeril's Homemade Mayonnaise

Ingredients

• 1 large egg, at room temperature
• 1 large egg yolk, at room temperature
• 1 1/2 teaspoons freshly squeezed lemon juice, or more to taste
• 1/2 teaspoon Dijon mustard
• 1/2 teaspoon minced garlic
• 1/2 teaspoon kosher salt, or more to taste
• 1/4 teaspoon ground white pepper or cayenne pepper, or more to taste
• 1 cup vegetable oil
• 1/4 cup olive oil