Place 1 cup of water in a medium saucepan and bring to a boil over high heat. Add sliced carrots, reduce heat to low, cover and simmer for 5 minutes.

Meanwhile, melt butter in a medium nonstick skillet over low heat. Add onion. Cook for 5 minutes, stirring occasionally.

Drain carrots and add to onions. Add broth and stir. When liquid has evaporated, add salt. Continue cooking, stirring occasionally for about 20 minutes. Remove from heat and sprinkle with Parmesan cheese. Stir to melt the cheese.