Prepare the shallots. In a large saute pan over medium heat, add butter and oil. Cook until butter has melted and starts to foam slightly. Stir in the shallots, season with salt and cook until soft and lightly golden brown, stirring occasionally, about 25 minutes. If the mixture starts to brown too quickly, stir in a few tablespoons of water and continue cooking
Stir in the vinegar and sugar and cook until caramelized, about 5 minutes longer. Season with pepper and more salt, if needed.
Preheat your grill for indirect grilling. If using gas, heat with main burners on high and hood closed for at least 10 minutes. Once hot (at least 500°F), turn off burners under the indirect zone. If using charcoal, place a single, dense layer of hardwood lump charcoal in one area of the Hybrid Fire Grilling Drawer(s) and leave the rest empty. Light all of the main burners on high and keep the hood open while charcoal fire starts. Once charcoal shows strong flames, turn off burners below charcoal. Turn off remaining burners once charcoal has settled to desired heat level. Heat the grill at least 45 minutes before starting to grill the steak.
Mix together the paprikas, cumin, mustard, fennel, coriander and pepper in a small bowl. Season the steak on both sides liberally with salt. Season the top side of the steak with a few tablespoons of the spice rub. Let sit at room temperature for 30 minutes.
Mix together the butter and garlic in a small bowl and season with salt and pepper. Grill the bread over direct heat on both sides until lightly golden brown, about 45 seconds per side. Remove to a flat surface and spread the garlic butter over one side of each slice. Set aside.
Before beginning, make sure that your grill has preheated for at least 45 minutes and it is registering a temperature of at least 500 degrees F.
Brush your steak on both sides with olive oil. Place steak on the grill and grill for 30 seconds, flip over and grill for 30 seconds longer. Rotate 90 degrees, flip over again and grill for another 30 seconds. Flip over and grill for 30 seconds longer. Move the steak to the indirect portion of the grill. Close the lid and use the grill like an oven. Continue grilling and turning the steak every 3 minutes until it reaches an internal temperature of 125 internal temp on a digital thermometer, about 12 to 15 minutes. Remove from the grill, let rest for 10 minutes then slice into thin slices.
Assemble the bruschetta. Divide the shallots evenly over the garlic toast, top with a few slices of thinly sliced steak and sprinkle with crumbled blue cheese.