1. For the Aioli, mix all ingredients in medium bowl; cover. Refrigerate until ready to serve.
2. For the Shrimp Cakes, mix flour, baking powder and Old Bay in large bowl. Stir in shrimp, cooked rice, green onions, dill seed and thyme. Add butter, milk and eggs; gently stir until well blended.
3. Spray large nonstick skillet with no stick cooking spray. Heat on medium heat. Drop heaping tablespoonfuls of shrimp mixture into skillet. Flatten slightly so cakes are about 2 inches in diameter. Cook cakes in small batches, 5 minutes per side, or until lightly browned.
4. Serve shrimp cakes with 1/2 of the Aioli. (Remaining Aioli may be used as a sandwich spread or as a dip for vegetables.)
To toast dill seeds: Heat small skillet on medium heat 2 minutes. Add dill seeds; cook 1 minute or until seeds are fragrant, shaking pan frequently. Immediately remove seeds from skillet to avoid over-toasting.
Make Ahead: Shrimp cakes can be made up to 24 hours ahead. Cool, wrap and store in the refrigerator. Reheat on baking sheet in preheated 350°F oven for 10 minutes. The aioli can be made up to 24 hours ahead. Refrigerate in covered container until ready to serve.