Heat the oil in a large nonstick skillet over medium-high heat.
Toss in the sausage and break up with a wooden spoon until brown.
Pour in the beans, tomatoes, salt, pepper, and thyme, and mix until everything has warmed through.
Move the contents of the pan out of the way to form an open well in the center of the pan. Pour the eggs into the well, and as the bottom of the eggs start to cook and solidify, use a spatula to gently scrape the cooked bits off the bottom and slowly mix with the other contents of the pan.
Add the spinach to the pan and mix.
Spoon a portion of the mixture onto a warmed tortilla, top with avocado slices and Greek yogurt, and roll the tortilla into a burrito.