PLACE A RACK IN UPPER-MIDDLE OF OVEN AND HEAT TO 400 DEGREES. LINE A BAKING SHEET WITH PARCHMENT AND SET ASIDE.
IN A LARGE BOWL, WHISK MUSTARD, 1 TBSP OIL, THE WORCHESTERSHIRE SAUCE, ANCHOVY, GARLIC, AND PEPPER UNTIL SMOOTH. BREAK BROCCOLI AND CAULIFLOWER FLORETS LARGER THAN 1" INTO SMALLER PIECES, THEN ADD VEGETABLES TO BOWL AND TOSS WELL TO COAT. TRANSFER TO PREPARED BAKING SHEET AND RESERVE BOWL.
ROAST UNTIL VEGETABLES ARE BROWNED IN SPOTS BUT NOT QUITE TENDER, ABOUT 10 MINUTES. MEANWHILE, COMBINE BREAD AND REMAINING 1 TBSP OIL IN NOW-EMPTY BOWL AND TOSS TO COAT. THEN ADD CHEESE AND TOSS AGAIN, SET ASIDE.
STIR VEGETABLES WELL, THEN PUSH TO ONE SIDE OF BAKING SHEET. SPREAD BREAD OVER EMPTY SIDE, THEN CONTINUE TO BAKE UNTIL VEGETABLES ARE TENDER AND CROUTONS ARE CRISPY, ABOUT 10 MINUTES.
TRANSFER VEGETABLES TO A PLATTER AND DRIZZLE WITH LEMON JUICE. SPRINKLE CROUTONS AND MORE CHEESE OVER TOP AND SERVE.