Wipe the portobello caps clean with a damp towel, remove stems and gently scrape gills if desired. Place caps and quartered red pepper in a shallow dish. In a small bowl whisk together 3 tbs olive oil, 2 tbs balsamic vinegar, minced garlic, dried oregano, 1 tsp kosher salt and 1 tsp black pepper. Pour marinade over mushrooms and peppers, turning to coat. Let sit 15 minutes at room temperature (or up to 30 minutes refrigerated).

Grill vegetables

Preheat grill or grill pan to medium-high (about 400°F / 200°C). Brush the grill grates with oil. Place portobello caps gill-side down first for 3–4 minutes then flip and grill another 3–4 minutes until tender and marked. Grill red pepper pieces skin-side down until charred (about 3–5 minutes per side). Remove vegetables to a cutting board, tent with foil and let rest 5 minutes. Slice each portobello into 3–4 strips; thinly slice red pepper into long strips.

Wilt the spinach

Heat a medium skillet over medium heat with 1 tbs olive oil. Add the packed 2 cups spinach and cook, stirring, until just wilted, about 1–2 minutes. Season lightly with a pinch of salt and transfer to a bowl.

For the balsamic glaze & finishing

Make the glaze by combining 1 cup balsamic vinegar and 1 tbs brown sugar or honey in a small saucepan. Bring to a gentle simmer over medium-low heat, then reduce heat to low and simmer uncovered for 10–12 minutes, stirring occasionally, until reduced to about 1/4–1/3 cup and syrupy (it will thicken more as it cools). Remove from heat and stir in 1 tsp butter if using for a glossy finish. Taste and season with a pinch of salt if desired. Let cool slightly.

For assembly

Toast buns: Spread softened butter on cut sides of 4 brioche buns. Toast on the grill or in a skillet over medium heat until golden, 1–2 minutes.

Spread: If using, spread 1 tsp mayonnaise on the bottom half of each toasted bun.

Layer the sandwich: Divide the wilted spinach evenly among the 4 bottom buns (about 1/2 cup spinach per sandwich). Top with 3–4 slices of grilled portobello per sandwich, then a few strips of grilled red pepper. Sprinkle about 3/4 oz bleu cheese crumbles on each sandwich (to total the 3 oz). Add 2 fresh basil leaves per sandwich if using.

Finish with glaze and close: Drizzle about 1 tbs of the balsamic glaze over the vegetables on each sandwich (adjust to taste). Close with the top bun and press gently to secure.

Serve: Serve warm. Provide extra balsamic glaze and additional bleu cheese at the table for guests who want more.