Bring a large pot of water to a raging boil. Add spaghetti and cook according to package instructions. Reserve 1 cup of the pasta water before draining.
In a large skillet, heat the olive oil over medium heat.
Add the garlic and red pepper flakes, cooking until fragrant, about 30 seconds. Be careful not to burn the garlic.
Add in the carrots and broccoli and cook until tender, about 5 to 7 minutes. Cover while cooking, stirring occasioally.
Mix the hummus with 1/4 cup to 1/2 a cup of the reserved pasta water. Add more water if necessary to create a thin sauce. Whisk in the lemon juice.
Combine the drained spaghetti, the sautéed vegetables, and the hummus sauce. Add the sliced green onions and the sesame seeds. Serve and enjoy!