Bring meat to room temperature, 1 to 1 1/2 hours. Meanwhile, make filling: Toast bread crumbs in a small frying pan over medium heat until deep golden brown, stirring, 4 to 5 minutes; let cool.
Set aside 2 tbsp. gorgonzola and 1 tbsp. parsley and chill. Combine bread crumbs, remaining cheese, 3 tbsp. parsley, 1 tbsp. chives, and 1 tsp. thyme in a bowl until well blended. Chill until cold, 1 hour.
Heat a grill to medium (350° to 450°) with a burner turned off (for gas) or coals pushed to sides of firegrate (for charcoal) to make an indirect-heat area. Cut a lengthwise slit down center of meat to within 1 in. of underside and 1/2 in. from ends, forming two sections. In each section, center a slit parallel to first, with the same depth and length. Densely pack the three slits with filling. Press cut sides together. Season roast with 1/2 tsp. each salt and pepper.
Lay meat cut side up. Wrap in bacon, overlapping ends under roast if bacon is long enough. Tie roast crosswise with kitchen twine at 1-in. intervals.
Grill beef, covered, over direct heat until lightly browned, turning as needed (watch carefully), 10 to 15 minutes. Move meat to indirect heat and cook, covered, until an instant-read thermometer inserted into thickest part of meat (not filling) reaches 135°, 25 to 35 minutes. Transfer to a platter, tent with foil, and let rest in a warm place 20 minutes.
Meanwhile, bring port and shallot to a boil in a medium saucepan over high heat. Reduce heat to medium and simmer until reduced to 1 cup, 20 to 30 minutes. Strain; discard shallot. Melt butter in a small saucepan over medium heat. Add flour and cook 2 minutes, stirring. Add port and bring to a simmer. Stir in remaining 1 tbsp. parsley, 1/2 tbsp. chives, and 1/2 tsp. thyme. Season to taste with salt and pepper.
Untie beef. Cut in 1-in. slices and arrange on a platter. Top with reserved gorgonzola and parsley. Pour some sauce around meat and serve remaining on the side.
*Center-cut beef tenderloin is a splurge, but you can cut the cost by butchering a whole untrimmed tenderloin yourself (it's easy). Learn how at sunset.com/beeftenderloin.