Heat oven to 375°F. Arrange bacon on a rack over a foil-lined rimmed sheet pan and sprinkle with brown sugar and 1/4 teaspoon pepper. Bake for 20 to 25 minutes until browned and crisp at the edges, then cool on the rack for 5 minutes.
Brush tomato slices lightly with olive oil and season with salt and the remaining pepper. Heat a grill pan over medium-high heat and cook tomatoes in two batches for 1 to 2 minutes per side until marked but still holding their shape.
Transfer tomatoes to a plate and cool for 5 minutes, then blot away loose juice. Mix mayonnaise, basil and lemon juice in a small bowl.
Reduce oven to 300°F and warm split croissants cut-side up for 5 minutes. Spread basil mayonnaise over the cut faces.
Place one dry romaine leaf on each bottom and add two grilled tomato slices and two bacon strips, breaking the strips only as needed to fit.
Close the croissants gently and serve promptly before the tomato moisture softens the pastry.