In 1-quart saucepan, place eggs. Cover with cold water 1 inch above eggs. Heat to boiling; remove from heat, then cover and let stand 18 minutes. Meanwhile, melt butter in 3-quart saucepan over medium heat. Remove stems from radishes, then cut radishes into 1/2-inch pieces. Add to saucepan along with thyme, and cook about 8 minutes, stirring occasionally, until tender.
Remove eggs from pan, and add to bowl of ice water until cool enough to peel. Peel eggs, then cut in half lengthwise.
Pull green leaves from radish stems, and add to cooked radishes along with sliced green onions. Cook about 1 minute or until leaves have wilted.
Assemble sandwiches by topping toasted bread with cooked radishes and radish leaves, egg halves, Parmesan cheese and lemon peel. Finish with a pinch of salt and some freshly ground pepper on top.