Preheat the oven to 350 degrees F.
Crack the eggs into a medium mixing bowl and pour in the cream. Add the chives, tarragon, salt and pepper and whisk until well incorporated and foamy.
Preheat an 8-inch skillet over medium heat. Add the butter and turn the heat down slightly. With a 4-ounce ladle, add one ladle of eggs to the pan. Immediately begin stirring with a spatula. (Cook's note: This is to heat the eggs through so they set like a custard. Keep swirling them around so the eggs aren't in one spot long enough to burn.)
Once the eggs begin to set, stop stirring. Transfer the pan to the oven for 1 1/2 minutes; the omelette should still have a soft custard touch
Top the omelette with the bacon, avocado and Monterey Jack. Return it to the oven for 30 seconds, just so the cheese begins to melt. Using an oven mitt to grip the handle, tip the pan sideways and roll the omelette onto a plate with the help of a spatula. Garnish with more chives and tarragon, and chervil.