Heat a dry skillet over medium heat. Add the pine nuts and sliced garlic. Toast for about 3 minutes, stirring often until the pine nuts turn golden and the garlic smells fragrant. Remove from heat and let cool.
Combine basil, avocado, cheese, lemon juice, pine nuts, and garlic in a food processor. Add salt and pulse until mostly combined.
While the processor is running, slowly stream in the olive oil, starting with 1/3 cup and adding more as needed to reach your preferred consistency.
Taste and adjust the seasoning if needed. Serve immediately as a sauce tossed with warm pasta or as a fresh spread on bread.