In a medium saucepan, cook green pepper and onion in butter till tender. Stir in flour, mustard, salt, oregano, thyme, and pepper; add milk all at once. Cook and stir till mixture is thickened and bubbly. Cook and stir 1 minute more. Cover and keep warm.
In a lightly greased 10-inch skillet heat 1-1/2 inches water to boiling; reduce heat so water simmers. Break ONE egg into a small sauce dish. Carefully slide egg into simmering water, holding lip of dish as close to the water as possible. Repeat with remaining 5 eggs, keeping them separate in the skillet. Simmer, uncovered, over low heat for 3 to 5 minutes or to desired doneness (do not let water boil).
Meanwhile, divide slices of Swiss cheese among toasted English muffin halves. Place on rack of an unheated broiler pan. Broil 3 to 4 inches from heat till cheese melts. When eggs are done, lift out of skillet with a slotted spoon, place each egg on a muffin half. Spoon some sauce over each. Sprinkle lightly with paprika and serve.