Heat a large deep skillet over medium heat. Add the butter and let it melt completely until slightly foamy. Stir in the minced garlic and cook for 30 seconds to 1 minute while stirring often. The garlic should smell fragrant but should not brown.
Add the dry orzo pasta to the skillet. Stir well so the pasta becomes fully coated in the butter and garlic mixture. Continue cooking for 1 to 2 minutes, stirring often, until some of the orzo looks lightly toasted and golden around the edges.
Slowly pour the chicken broth into the skillet while stirring the orzo. Bring the mixture to a gentle boil over medium heat.
Reduce the heat to medium-low and allow the orzo to simmer for 10 to 12 minutes. Stir every few minutes so the pasta cooks evenly and does not stick to the bottom of the pan. Continue cooking until the pasta becomes tender and most of the broth is absorbed.
Lower the heat to low. Stir in the heavy cream and basil pesto until fully combined. The sauce should become creamy and evenly mixed throughout the pasta.
Add the parmesan cheese, lemon juice, salt, and black pepper. Stir slowly until the cheese melts completely into the sauce and the orzo becomes creamy and glossy.
Taste and adjust seasoning if needed. If the sauce becomes too thick, stir in a splash of warm broth or cream.
Sprinkle fresh parsley over the top before serving. Serve warm with extra parmesan cheese if desired.