Make the Crust: Combine flours and salt in the work bowl of a food processor and process to combine. Scatter butter cubes over the top of the flour mixture and pulse until mixture resembles coarse sand with a few pea-sized pieces of butter here and there, about 8-10 pulses. Transfer mixture to a bowl and sprinkle the ice water over the top. Mix with a fork and/or your fingers until no dry spots remain and the dough holds together when squeezed.
Transfer dough to a piece of plastic wrap. Gather into a ball and press into a disk, about 5 inches in diameter. Chill for at least two hours or up to two days before rolling.
Make the Filling: Using your hands, gently toss tomato slices in a large colander with 1 teaspoon salt. Set over a sink to drain for 30 minutes.
Preheat oven to 375 degrees. Transfer chilled dough round to a piece of parchment paper. Dust the top of the dough round with flour to prevent sticking. Using a rolling pin, roll into a 12 inch circle. Trim the edges with a pizza wheel if desired. Transfer to an inverted baking sheet leaving parchment paper in place. Place in the refrigerator for 20-30 to firm up slightly.
Meanwhile, shake colander to get rid of any accumulated water. Combine tomatoes, shallot, oil, thyme, garlic and few grinds of freshly ground pepper and ½ teaspoon salt in a large bowl. Remove dough round from the refrigerator and place the dough round and parchment inside the rimmed baking sheet. Spread mustard over the surface of the dough, leaving a 1 ½ to 2 inch border around the edges. Sprinkle Havarti cheese in an even layer over the mustard.
Using your hands, arrange tomato mixture on the bottom of the tart in concentric circles, continuing to leave a 1 ½ to 2 inch border around the edge. Leave any accumulated juices behind in the bowl. Sprinkle with parmesan.
Fold the border of the dough inward over the tomato mixture so that it covers the filling by about 1 inch, overlapping the dough every couple of inches. Gently press dough so that it adheres. Brush with beaten egg.
Bake until crust is golden brown and filling is bubbly, about 50 minutes. Transfer baking pan to a wire rack to cool. Sprinkle with basil. Cut into wedges and serve.