Combine garlic and 1 tablespoon butter in a microwave-safe bowl. Cover with plastic wrap, microwave on high 2 minutes or until soft, and let cool. Repeat with shallots and 1 more tablespoon butter.
Beat remaining butter at medium speed with a mixer until light and fluffy. Add garlic butter, shallot butter, and remaining ingredients; beat until combined. Form into a 1 1/2-inch-thick log. Chill until firm. (Remaining butter can be stored in the freezer for 1 month.)