In an 8- to 9-inch-wide pan, bake nuts in a 350° oven, stirring often, until golden, 5 to 7 minutes; let cool.
In a bowl, combine whole-wheat flour, 1 cup all-purpose flour, thyme, and 1 teaspoon salt. With a pastry blender or your fingers, cut or rub in butter and shortening until particles are pea-size. Stir in pine nuts. With a fork, gently stir in 1/2 cup ice-cold water, 1 tablespoon at a time.
Gather dough into a ball, divide in half, and flatten each portion into a 1-inch-thick disk. Wrap airtight and chill at least 45 minutes or up to 2 days.
On a board dusted with all-purpose flour, roll dough pieces, one at a time, into 11-inch rounds. Fit each round into a 9-inch tart pan with a removable rim; trim excess dough from rim.
Fit a piece of foil into each crust, with foil edges extending at least 2 inches above rim. Pour dried beans or pie weights into foil to half-fill crusts. Bake on the lowest rack in a 375° oven for 30 minutes. Remove foil and beans.
Overlap tomatoes in circles in hot crusts. Bake until tomatoes look dry at edges, about 15 minutes.
Meanwhile, in a bowl, whisk eggs, pesto, goat cheese, and 1/2 teaspoon salt to blend, then whisk in cream. Gently pour mixture equally over tomatoes.
Bake until custard is set when gently shaken, about 25 minutes. Season to taste with salt. Serve hot or cold.