Preheat a grill or grill pan over medium-high heat. Season the steak and grill, about 6 minutes per side for medium-rare. Let rest.
Lower heat to medium; wrap the garlic in foil and cook until soft, 15 minutes. Grill chiles 6 minutes, turning occasionally.
Squeeze the garlic from its skin into a food processor. Stem and seed the chiles then add to garlic along with EVOO, lime juice and sugar. Pulse to a paste and season with salt.
Brush cut sides of the bread with EVOO and toast on the grill. In a bowl, stir together the mayo, lime zest and 3 tbsp. water.
Thinly slice the steak. Spread chile paste on baguette bottoms and some lime mayo on baguette tops. Divide the steak and spinach among sandwiches.
