In a medium saucepan over medium-high heat, saute garlic and onion in butter until fragrant and caramelized, about 5 minutes. Reduce heat to medium and whisk in flour. Slowly whisk in milk and chicken broth until sauce is smooth. Bring sauce to a simmer over medium heat, stirring occasionally until slightly thickened. Remove from heat and whisk in pesto until smooth.

Place spaghetti in a 9x13 baking pan and pour half of sauce over top and gently stir to coat. Meanwhile, stir peas and chicken into remaining sauce. Make a well down the center of spaghetti and slowly spoon sauce down the middle. Sprinkle top with cheese and breadcrumbs.

Cover pan with foil and refrigerate tetrazzini up to 3 days. (tetrazzini may also be frozen up to 2 months) When ready to bake, remove tetrazzini from fridge or freezer and bake, covered with foil at 350F 20-25 minutes, then remove foil and bake an additional 5-10 minutes until breadcrumbs are toasted and filling is bubbly. (if baking directly from the freezer, increase the bake time to 30-35 minutes) Enjoy tetrazzini hot!