Make the galette dough. Add the flour, everything bagel seasoning, salt and butter to a food processor and pulse (do not run, pulse quickly and in short bursts) until fine crumbs form.
Slowly add in ice water, 1 tablespoon at a time, and pulse each time until the dough just comes together. Should be somewhat moist, but not wet.
Remove the dough from the processor, shape into a round flat disc and refrigerate at least one hour or up to overnight.
When ready to bake, preheat the oven t0 375 degrees.
Lay the dough on a sheet of parchment paper, and cover with another sheet of parchment, or plastic wrap. Roll out the dough between 2 sheets of parchment to ¼” thickness, turning clockwise as you roll it out to retain the round shape.
Remove the plastic wrap or top later of parchment, and transfer the dough (on the parchment) to a large baking sheet.
Spread the pimento cheese over the center of the dough, leaving about a 2 inch edge,
Layer the tomatoes on top of the pimento cheese, cut side up- pressing lightly into the cheese spread to keep them secure.
Carefully pull the crust up and over to form an edge, working clockwise and overlapping to seal.
Brush the outer edges of the dough that you have folder up with beaten egg, and sprinkle 1 teaspoon of everything bagel seasoning liberally over the egg washed edge.
Top the tomatoes and pimento cheese with grated cheddar and bake for 50-55 mins at 375 degrees until crust is golden brown and cheese is well browned, rotating the pan halfway through to promote even browning.
Check on the galette periodically. If crust becomes too dark, tent with foil.
Allow to cool 15-20 minutes prior to serving. Serve warm, room temp or cold.