While the caramel hardens, work on the flan. In a medium mixing bowl, add egg yolks, condensed milk, and vanilla. Whisk together until fully combined.
Slowly add evaporated milk while whisking.
To make extra smooth flan, strain the mixture by pouring it into another container through a fine mesh sieve. I like to strain mine into my 4 cup liquid measuring cup, since this recipe makes about 3 cups of liquid and the measuring cup has a spout for easy handling!Pour flan mixture into baking dishes with the hardened caramel. Place baking dishes into a larger roasting pan. Pour water into roasting pan so that the baking dishes are sitting in at least 2 inches of water. Cover the baking dishes with aluminum foil.
Place roasting pan with covered flan into the preheated oven. Depending on the size of your baking dish, baking time may vary from 30-60 minutes. At the 30 minute mark, check if the flan is done: the center should still jiggle slightly, but the top should feel a bit firm to the touch. Stick a cake tester or toothpick in the middle of the flan. If it comes out clean, it can be removed from the oven. If not, check flan every 5-10 minutes.
Remove from oven and take baking dishes out of the roasting pan, placing them on a cooling rack. Allow to cool until room temperature, then cover and refrigerate until completely chilled, at least 3 hours.
Run knife around the edges of the flan to loosen it, then invert the dish onto a rimmed tray (to catch the extra caramel) lined with parchment paper. Some hard caramel will stick to the baking dish—it's completely normal and happens to most people. For easier clean up, soak the dish in hot water, changing the water whenever it cools down.
Use 4-inch cookie cutter to cut out the bear's head, then use the 1.5-inch cookie cutter to cut out two ears. Place the head and ears onto your serving dish.