In a medium saucepan, combine the butter, mustard, salt, and water. Heat over medium until the butter melts and the mixture is just shy of boiling.

Add the flour all at once, stirring vigorously with a wooden spoon. Cook, stirring constantly, until the dough pulls away from the sides of the pan, about 2 minutes.

Transfer the dough to a stand mixer fitted with the paddle attachment. Mix on low speed for a few minutes to cool slightly.

Gradually add the Parmesan and eggs, one at a time. The dough may separate at first but will come together into a smooth, glossy paste. The consistency should resemble thick choux pastry—soft yet pipeable. If too stiff, mix in another egg.

Transfer the dough to a piping bag and refrigerate for 30 minutes.

Lightly flour a work surface. Pipe long ropes of dough, then use a knife to cut into small, bite-sized pieces. Toss lightly in flour and transfer to a parchment-lined tray. Freeze until ready to cook.

In a large skillet, heat a drizzle of olive oil over medium heat. Add the garlic and cook until fragrant, about 1 minute. Stir in the cherry tomatoes and cook on low heat until soft and jammy, about 20 minutes.

Pour in the wine and gently mash the tomatoes with a spoon. Season with salt and stir in the basil.

Bring a large pot of salted water to a boil. Add the gnocchi in batches, cooking until they float, about 3 minutes. Use a slotted spoon to transfer them directly into the sauce.

Stir in the butter, allowing it to melt and emulsify into the sauce. Toss gently to coat the gnocchi in the glossy tomato butter. Serve immediately, garnished with extra basil and Parmesan. Enjoy with a glass of chilled white wine.