Add carrots to a saucepan and cover with water. Boil until fork-tender, about 20 minutes.

Drain carrots, place into a large bowl, and mash into a paste using a potato masher.

Add the flour, parmesan, egg, 1 clove grated garlic, thyme, and 1 teaspoon salt to the carrots. Combine until a dough ball forms.

Transfer the dough to a floured surface and knead gently until firm and workable.

Cut dough into 4 sections. Roll each section into 1-inch ropes.

Slice each rope into ½-inch pieces.

If desired, roll gnocchi on a rigagnocchi, creating grooves in the dumplings.

To cook the gnocchi, bring a large pot of water to boil. Working in batches, cook gnocchi in boiling water until soft, about 1-2 minutes.

Melt 1 tablespoon butter in a large skillet. Add drained gnocchi and walnuts and cook until both are browned, about 4-5 minutes.

Remove the gnocchi and walnuts from the skillet. Add the remaining 7 tablespoons butter.

Cook butter over medium heat until browned, stirring often, about 5-10 minutes. Add the remaining grated garlic and salt, and stir to combine.

Pour browned butter over gnocchi. To serve, top with grated Romano.