Cook bacon until crispy, then crumble and set aside.
Whisk eggs and heavy cream together with salt and pepper until well combined.
Melt butter in a skillet over low heat.
Pour egg mixture into the skillet, stirring frequently until soft and pillowy.
Warm the low-carb tortillas in a separate pan.
Assemble by filling each tortilla with eggs, crumbled bacon, cheese, and sliced avocado.