Preheat oven to 375 degrees Fahrenheit.
In small bowl, combine oil with garlic and basil, salt and pepper. Brush oil mixture over zucchini, red and yellow pepper slices. Place zucchini in grill pan set over medium high heat; grill, turning once and basting with some of leftover oil mixture, for eight minutes or until softened. Remove from pan. Repeat with red pepper and remaining oil mixture, cooking peppers for five to seven minutes per side.
Meanwhile, cut each sheet of phyllo in half crosswise. Place one half on tea towel, keeping remaining covered with damp towel. Brush sheet with some of melted butter; place another sheet on top, a little askew so they are not perfectly aligned. Brush with melted butter. Top with another sheet of phyllo, slightly askew again. Brush with butter. Repeat one more time. Lay another sheet of phyllo on top; brush with half of Dijon mustard. Layer another half sheet of phyllo on top; brush with remaining Dijon mustard. Keeping phyllo slightly askew, repeat layers, brushing last two layers with melted butter. Transfer to 14 – x 4-1/2 inch French tart pan with removable bottom. Fold phyllo edges under.
Sprinkle breadcrumbs onto bottom of prepared tart, sprinkle with cheese. Layer with half of zucchini and half of sweet peppers. Spread half of prepared pesto over vegetables. Sprinkle with half of cheese. Repeat layering once, ending with cheese.
Bake in centre of preheated oven until phyllo is golden and cheese is completely melted, 25 to 35 minutes.