Adding the preparation half, which decides how much water you brought to the fight.
Dry everything. Washed vegetables carry a lot of surface water and every drop has to boil off before browning can start. A tea towel or a spin in a salad spinner is thirty seconds and it changes the result.
Cut evenly, and not too small. Uneven pieces mean some are burnt while others are raw, which pushes people to lower the heat. Slightly larger pieces survive high heat better.
Salt at the right moment. Salt draws water out. Salting well before cooking gives you a wetter pan; salting at the end or once browning has started avoids that. For roasting it matters less; for a hot pan it matters.
Do not stir constantly. Contact time is what browns. Put things down, leave them alone for a minute or two, then move them. Continuous stirring keeps everything just below the temperature where anything interesting happens.
Use enough fat. Fat conducts heat into the surface. A dry pan browns unevenly and sticks, and people then add more vegetables to stop the sticking, which makes it worse.
And if the pan is genuinely full and you cannot batch - put it in a hot oven instead. Roasting works fine at volume and the mechanism is the same.