In a large sauté pan over medium-high heat, add the olive oil and shallots. Cook for 1 to 2 minutes until the shallots start to become soft. Add the mushrooms, thyme, salt, and pepper. Cook until the mushrooms start to brown, approximately 5 minutes. Drizzle in the balsamic vinegar and continue to cook until the mushrooms are caramelized, approximately 2 minutes longer.
Place the bread slices in your toaster or toaster oven. Toast until just brown and crunchy.
Slice the avocado in half lengthwise and remove the pit. Using a soup spoon, scoop the flesh out of each half. Slice the avocado thinly from end to end into half-moons.
Layer the avocado slices on each piece of toast. Spoon the mushrooms over the avocado. Season each toast with a pinch of coarse or kosher salt.