When deep-frying, choose an oil with a high smoke point, such as canola or peanut oil.
Sauté sausage in a large skillet over medium heat 3 to 4 minutes or until crisp. Add onion and next 2 ingredients; sauté 3 to 4 minutes or until vegetables are tender. Remove from heat, and stir in rice and next 3 ingredients. Cool 30 minutes. Stir in 2 large eggs and breadcrumbs.
Gently press rice mixture evenly around hard-cooked eggs to cover, using wet hands.
Pour oil to depth of 2 inches into a Dutch oven; heat over medium heat to 360°. Fry eggs, in 3 batches, 3 minutes or until golden brown, turning often. Drain on a wire rack over paper towels.