Peel the shallots and place in a small saucepan. Cover with oil and cook over low heat until the shallots become very soft and translucent, about 1 hour. (The shallot confit can be refrigerated in an airtight container up to 2 weeks.)
Preheat the broiler to medium-high.
In a small bowl or cup, mix together the honey and mustard. Season the salmon with salt and pepper. Brush each piece with 1 tablespoon honey-mustard glaze.
Place the salmon on a foil-lined baking sheet. Place in the broiler and cook, brushing with more glaze halfway through, until just a bit translucent in center, 7 to 9 minutes.
Place the salmon and shallot confit on a platter and garnish with parsley sprigs. Serve with spinach on the side.
