Mince garlic.
Cut broccoli lengthwise into slices, about ¼ inch thick.
Cut ends off red onion and discard peel. Quarter lengthwise, cut a quarter of the onion lengthwise into strips, about ¼ inch thick.
Rinse shrimp. Pat dry with paper towels.
Heat 1½ tablespoons cooking oil in a medium sauté pan over medium heat. Add tofu and garlic to hot pan. Season with ¼ teaspoon salt and a pinch of pepper. Cook 4-5 minutes, or until tofu is fully cooked and garlic is fragrant, stirring occasionally.
Add toasted sesame oil and half the chili flakes to pan with tofu. Cook 1-2 minutes, stirring frequently.
Remove from heat. Add black and white sesame seeds. Stir to coat.
Heat 2 tablespoons cooking oil in a large sauté pan over medium-high heat. Add broccoli and onion to hot pan. Season with ¼ teaspoon salt and a pinch of pepper. Cook 3-4 minutes, or until broccoli begins to brown, stirring occasionally.
Add cabbage and carrots, roasted cashews, and about 2 tablespoons water. Cook 2-3 minutes, or until veggies are tender and water has evaporated, stirring occasionally.
Divide broccoli stir fry between plates and top with sesame tofu. Drizzle with spicy aioli to taste.