In a large stock pot, boil water and place the steamer on top of the water.
In a small bowl, whisk the egg yolks, evaporated milk, and sweetened condensed milk until just combined and smooth. Add the vanilla and mix well.
Put the llanera over the stove on low heat. Add the brown sugar and water to the llanera and mix until combined. Heat over the stove until the sugar mixture has a liquid syrup texture. Please handle carefully as the llanera will get hot.
Remove the llanera from the stove. Rotate the llanera so that the sugar mixture evenly coats the bottom. Strain the egg mix through a mesh strainer over the llanera. The egg mix will be strained directly on top of the sugar mixture in the llanera. Please note this mixture will yield extra. The llanera will only need to be filled about ¾ of the pan. (The extra will be just enough for a small ramekin that can be cooked separately. Start to check for readiness at the 30 minute mark due to its size.)
Cover the llanera with aluminum foil. Put in the steamer over boiling water and steam for 60-65 minutes until a knife inserted halfway through pulls away clean.
Remove the llanera from the steamer and let it cool for at least 40 minutes. Before serving on a plate, run a thin knife along the edges to loosen the flan. Serve room temperature or refrigerated. Enjoy!
