Make avocado crema. Combine avocado, yogurt, cilantro, and lime juice in a blender and puree until smooth. Season with salt and pepper and set aside.
Prepare chicken patties. Combine ground chicken with brown sugar, thyme, salt, paprika, onion powder, cayenne, oregano, black pepper, and garlic in a large bowl. Mix until well combined and form 6 patties. Set aside.
Heat 1 tablespoon oil in a large saute pan over medium heat. Add halved cherry tomatoes and cook until tomatoes soften, about 4-5 minutes. Season with salt and pepper and set aside.
Wipe pan clean and add another tablespoon of oil. Cook eggs until soft scrambled and season with salt and pepper. Remove from heat and keep warm.
In the same pan, heat another tablespoon of oil. Lay the chicken sausage and cook until browned. Flip, lay sliced cheese on top and cook until the cheese melts. Remove from heat.
Assemble sandwiches. Spread avocado crema on the bread slices and top half of them with arugula. Place sausage, eggs, blistered tomatoes, and remaining bread on top. Serve immediately.
Notes
You can use sliced white bread, English muffins, bagels, or croissants for the bread.