How to Make It
In a medium saucepan, combine the olive oil with the tomatoes, thyme, bay leaf and half of the garlic and bring to a simmer. Cook over low heat until the tomatoes are very tender, about 15 minutes. Discard the thyme and bay leaf. Using a slotted spoon, transfer the tomatoes to a work surface and coarsely chop them; reserve the olive oil for another use.
In a large saucepan, melt the butter. Add the onion and a pinch of salt and cook over moderate heat, stirring, until softened, 5 minutes. Add the pasta and cook, stirring, until golden in spots, about 2 minutes. Add the remaining garlic; cook for 1 minute.
Add 1/2 cup of the chicken stock to the pasta and cook over moderately high heat, stirring constantly, until nearly absorbed. Continue adding the chicken stock, 1/2 cup at a time, stirring and cooking until it is nearly absorbed between additions. The pasta is done when it is al dente and suspended in a lightly thickened sauce, about 17 minutes total.
Stir the tomatoes into the pasta. Off the heat, add the goat cheese and Parmigiano-Reggiano and stir until melted. Season with salt and pepper, stir in the chives and basil and serve right away, passing additional Parmigiano-Reggiano at the table.