Preheat the oven to 350°F (175°C). Prepare two 6-inch round pans or llaneras.
Melt the sugar in a small pot over medium heat. Gently swirl until dark golden brown. Immediately divide between the molds and tilt to coat the bottoms. Use oven mitts — the molds will be hot.
Gently whisk the egg yolks and whole eggs in a bowl. Add the evaporated milk, condensed milk, and vanilla. Whisk until combined. Avoid beating until foamy.
Strain the custard into the caramel-lined molds. Skim off any foam.
Place the molds in a large, deep baking pan. Set it on the oven rack, then carefully add hot water halfway up the sides of the molds. Keep water out of the custard.
Bake uncovered for about 45 minutes. The edges should be set and the center should jiggle slightly. A thin knife inserted near the center should come out clean.
To steam instead: Skip the water bath. Cover the molds with foil and steam over medium-low heat for about 30 minutes, keeping the water gently bubbling. Check for doneness the same way.
Cool in the molds until no longer warm. Cover and refrigerate for a few hours or overnight, until fully chilled.
Run a thin knife around the edges. Place a rimmed serving plate over each mold, hold firmly, and flip. Lift off the mold and serve chilled.