Preheat oven to 325°F (170°C).

In a small saucepan, combine sugar and ⅓ cup (80 grams) water. Bring to a boil over medium-high heat, being careful not to splash sides and gently stirring frequently to help sugar dissolve. (Use a wet pastry brush to help dissolve any sugar that sticks to sides of pan.) (Do not stir once mixture starts to boil.) Cook until mixture turns a deep amber color. Immediately divide caramel among 6 (6-ounce) ramekins; carefully swirl ramekins so bottoms are evenly coated with caramel. (Sides of ramekins may be hot.) Place ramekins in a 13×9-inch baking pan.

In a large bowl, whisk together eggs and egg yolks until well combined. Add condensed milk and all remaining ingredients; gently whisk until well combined, stopping to scrape sides of bowl and being careful not to incorporate too much air. Strain through a fine-mesh sieve into a large bowl or glass measuring cup.

Spray sides of each ramekin with cooking spray; using a paper towel, spread into an even layer and wipe away any excess. Divide egg mixture among prepared ramekins (about 152 grams each). Using a small spoon, skim off any bubble clusters on surface, if desired. Cover each ramekin tightly with a square of foil. Add enough hot water to baking pan to come halfway up sides of ramekins.

Bake until set but still jiggly and an instant-read thermometer inserted in center registers 170°F (77°C) to 175°F (79°C), 35 to 38 minutes. Transfer flans to a wire rack; uncover ramekins, and let cool for 45 minutes. Cover and refrigerate for at least 4 hours or up to overnight.

Let chilled flans stand at room temperature for 45 minutes. To serve, place a plate upside down on top of 1 ramekin; invert, and remove ramekin. (See Notes.) Repeat with remaining ramekins.