In a skillet over medium-low heat, warm 1 tablespoon of the olive oil. Add the onion and garlic; sauté until soft, 10 to 15 minutes. Add the beans, bean broth, and thyme leaves; stir to combine and remove from heat. Add the lemon zest and juice.
Use an immersion blender to puree the mixture until smooth, or let cool slightly and process in a blender or food processor. Taste and adjust seasoning.
Preheat oven to 400°F. On a baking sheet, arrange the bread slices and drizzle with olive oil. Place in the oven; bake until light golden, about 10 minutes.
While the bread is baking, cook the mushrooms: Wipe the skillet dry and rewarm over medium heat. Add the remaining olive oil and the butter; heat until melted. Add the mushrooms; cook until soft and fragrant, 8 to 10 minutes. Season to taste with salt and pepper.
Remove the bread from the oven and flip the slices over. Spread the bean mixture onto each toast, then pile the mushrooms on top. Top with cheese and red chile flakes (if using), and return the sheet to the oven until cheese has melted and mushrooms are warm, about 5 minutes. Serve garnished with more fresh thyme.