Add garlic cloves to food processor and pulse 5-6 times until roughly chopped. This prevents large garlic chunks in the final pesto.
Add pine nuts (or sunflower seeds) and pulse 8-10 times until coarsely ground. The texture should resemble coarse breadcrumbs, not powder.
Add fresh basil leaves, salt, and pepper. Pulse 10-12 times until basil is roughly chopped and ingredients are combined.
With processor running, slowly drizzle in olive oil through the feed tube. Process for 15-20 seconds until mixture reaches desired consistency - it should be smooth but retain some texture.
Add grated Parmesan cheese (or nutritional yeast) and lemon juice. Pulse 3-4 times just to incorporate. Avoid over-processing at this stage.
Taste and adjust seasoning with additional salt, pepper, or lemon juice as needed. For thinner consistency, add olive oil 1 tablespoon at a time while pulsing.