Start by boiling about 1-2 quarts of water. You need to have this ready to use for the water bath. Of course, depending on the size of your baking pan, the quantity of water will vary. Then, preheat the oven to 300 degrees Fahrenheit or 150 degrees Celsius.
Add the heavy cream to a large enough saucepan and turn on medium-high heat. Heat the heavy cream until tiny bubbles start forming around the edges. Make sure you don't bring it to a boil, though. "Simmer" is the keyword.
Next step, as the cream is heating up, add the eggs and the erythritol in a medium-sized bowl. Whisk until the erythritol is properly incorporated. Once the cream is ready, remove it from the heat and pour it slowly into the egg mixture. Mix until well combined. Don't pour it all at once or too hot because you don't want to cook the eggs your custard.
Now that the custard is ready, add the vanilla bean paste or vanilla extract. Then, pour it into 4 ramekins and place them in an oven-safe pan. After that, pour the boiling water in the pan, about halfway up. Bake the keto creme brulee with quail eggs for about 40 minutes. You'll know they're cooked when the custard jiggles slightly when shaken.
Remove the ramekins and let them cool at room temperature for 15 minutes. Then, place them on a fridge for at least 1 to 2 hours. When they are ready to serve, sprinkle some erythritol over the top of the ramekins. Use a kitchen torch to caramelize it. Let it sit in the fridge for half an hour until it hardens. Enjoy!