Remove leaves and stems from radishes; trim the tails. Cut larger radishes lengthwise into sixths and smaller radishes lengthwise into quarters.
Place a large skillet over medium-high heat until very hot. Add 1 tablespoon oil, radishes in a single layer (do not crowd) and salt and pepper. Cook radishes, without moving them, until they are lightly colored on undersides, about 3 minutes. Shake pan and continue cooking until tender, about 3 more minutes. (You can also roast them in the oven at 400 degrees for 10 to 20 minutes.)
In a small skillet over medium heat, melt butter. Stir in anchovies, garlic, red pepper and remaining oil. Reduce heat and simmer about 4 minutes.
Brush each slice of toast with sauce and top with several radish wedges. Spoon additional sauce on top, sprinkle with parsley and serve.