Cook pasta to al dente according to the package instructions; drain, reserving the liquid.
Cut broccoli into bite-sized pieces and mince garlic.
Bring the pasta water back to a boil, then add the broccoli and cook for 2-3 minutes until bright green in color. Drain water out and cool down broccoli with ice cold water. Add pasta back to the pot and set aside.
Place a small saucepan over medium-high heat. Add olive oil and allow to heat for 1 minute.
Stir in garlic, sugar, vinegar, soy sauce, sesame oil, and chili sauce. Bring to a boil, stirring constantly until sugar dissolves.
Pour sauce over linguine and broccoli; toss to coat, then place over medium and cook until heated through.
Garnish with chopped green onions and sesame seeds. Serve with cherries on the side.