Heat olive oil in a large skillet over medium-high heat. Season chicken pieces with salt and pepper, then cook for 6-7 minutes until golden on all sides, stirring occasionally. Remove chicken to a plate and set aside for later.
In the same skillet, melt butter over medium heat and add minced garlic. Sauté for 1-2 minutes until fragrant, stirring constantly to prevent burning and develop aromatic flavors.
Pour in chicken broth and bring to a gentle simmer. Add the pesto and stir thoroughly, combining it with the buttery garlic base for approximately 2 minutes to ensure even distribution.
Return the chicken to the skillet and stir in heavy cream. Allow this garlicky buttery pesto chicken pasta sauce to simmer for 3-4 minutes until slightly thickened and chicken is heated through completely.
Meanwhile, cook pasta according to package directions in salted boiling water. Drain pasta when al dente and reserve 1/2 cup of pasta water for sauce consistency adjustment.
Add drained pasta directly to the skillet with the chicken and sauce. Toss gently to coat every strand, adding reserved pasta water gradually if the sauce seems too thick. Stir in parmesan cheese, lemon juice, and cherry tomatoes.
Cook for 1-2 minutes until tomatoes begin to soften slightly. Taste and adjust seasonings as needed, then transfer to serving bowls.
Garnish with fresh basil, toasted pine nuts, and extra parmesan. Serve immediately while the pesto chicken pasta is hot and aromatic.