Combine 1/2 cup raspberries, crème de cassis, and sugar in a small saucepan over medium heat; bring to a simmer. Cook 5 minutes or until raspberries are very tender; cool to room temperature. Press raspberry mixture through a fine sieve into a bowl, reserving liquid; discard solids. Combine raspberry liquid, shallots, and next 6 ingredients (through salt) in a medium bowl, stirring with a whisk.
Combine remaining 1 1/2 cups raspberries, mixed salad greens, and remaining ingredients in a large bowl; add shallot mixture, tossing gently to coat greens. Serve immediately.