In a skillet over medium heat, melt butter with olive oil.
Add onion and cook for 5-6 minutes, until softened.
Stir in garlic and orzo. Cook for 2-3 minutes, until lightly toasted.
Add chicken broth, heavy cream, and lemon juice. Bring to a gentle simmer.
Cook uncovered for 8-10 minutes, stirring occasionally, until orzo is tender and most liquid is absorbed.
Remove from heat and stir in Parmesan until creamy.
Assemble
Serve salmon over creamy lemon orzo. Garnish with parsley and serve immediately.