Place each puff pastry square in muffin tin and gently lift and press dough into cups. Dough should cover bottoms and sides with corners of each dough square sticking over edges. Refrigerate. While puff pastry chills, combine liquid egg, milk, 1/4 tsp. salt, and a pinch of pepper in a mixing bowl.

Coarsely chop roasted red pepper and 1/4 the spinach (reserve remaining for salad). Rinse and coarsely chop artichokes. Combine roasted red pepper, chopped spinach, and artichokes in another mixing bowl. Peel and halve shallot. Cut into 1/4" slices.

Remove muffin tin from refrigerator and add half the cheese to puff pastry squares. Add vegetable mixture, followed by egg-cream mixture. Top squares with remaining cheese. Roll and crimp quiche edges and place muffin tin on prepared baking sheet to catch any drips. Bake until dough browns and filling is set (doesn't jiggle when pan is tapped), 20-25 minutes. Rest quiches 5 minutes before carefully removing from muffin tin.

When quiches have 10 minutes left to bake, place a medium pan over medium-high heat. Add 2 tsp. olive oil, shallot, and grape tomatoes to hot pan. Stir occasionally until shallot is lightly caramelized and tomatoes are blistered, 3-4 minutes. Season with 1/4 tsp. salt and a pinch of pepper, remove from burner, and let cool 5 minutes.

Stir in remaining spinach to pan with tomatoes and shallots. Season with a pinch of salt and pepper. Spinach may wilt slightly from residual heat - it'll be just as good!

Serve salad on a plate alongside quiches.