Crust: Cook 3/4 cup butter in heavy small saucepan over medium heat until butter turns golden brown (nut-colored), watching carefully to prevent burning, about 4 minutes. Remove from heat. Pour melted brown butter into 1-cup glass measuring cup. Let melted butter stand until barely warm, 15 to 20 minutes.
Meanwhile, position rack in center of oven and preheat to 375°F Butter bottom and sides of 9-inch-diameter tart pan with removable bottom. Whisk flour, brown sugar, and salt in medium bowl to blend. Add 1/2 cup of barely warm melted brown butter and stir with fork until moist dough forms (mixture will resemble wet sand). Transfer dough to prepared tart pan. Using fingertips, press dough firmly and evenly onto bottom and up sides of pan (dough will look glossy). Let crust rest 5 to 10 minutes at room temperature. Bake crust until set and just golden brown, 15 to 18 minutes.
Filling: Meanwhile, whisk egg and brown sugar in medium bowl until well blended. Whisk in golden syrup, whipping cream, and salt. Stir in remaining melted brown butter, leaving most of darkened solids behind in bottom of measuring cup. Stir in pecans. Pour filling into warm crust, distributing pecans evenly.
Bake tart until filling is browned and slightly puffed and set at edges (center will still move slightly when pan is gently shaken), 25 to 27 minutes. Cool tart completely in pan on rack (center of filling will set as tart cools). (DO AHEAD Can be made 1 day ahead. Cover loosely and store at room temperature.).