Preheat oven to 450°F.
On a sheet pan, combine tomatoes, olive oil, salt and pepper. Roast in oven for 8-10 minutes or until tomatoes have blistered and popped open.
While tomatoes are roasting, bring to boil 2 quarts of water with 1 tablespoon of salt.
To make brown butter, heat butter in a large skillet over medium heat, watching for signs that it is nearly browning—it will become foamy, have a nutty aroma and toasty bits will appear at the bottom of the pan. Swirl and stir as needed for even browning.
Once the butter is brown, add diced squash and garlic and sauté for 2-3 minutes until the garlic is fragrant and the squash begins to soften. Add roasted tomatoes to the pan, including any accumulated juices, which will mix with the brown butter to make a sauce for the dish.
When salted water is at a rolling boil, add gnocchi and stir so they don’t stick together. Cook for 2 to 3 minutes, or until gnocchi are tender and begin to float. Using a strainer, remove gnocchi from water and add them to the skillet with tomatoes, squash and brown butter. Stir to combine, then simmer for 1-2 minutes, so gnocchi can absorb some sauce. Taste and adjust seasoning if necessary.
Garnish with torn basil and crumbled goat cheese.
