In a large bowl, sprinkle yeast over warm water; let sit until foamy, about 10 minutes. Stir in yogurt, oil and honey with a wooden spoon until well combined. Add flour, 3 teaspoons basil and salt; mix until flour is incorporated, 2 to 3 minutes. Turn dough out of bowl onto a lightly floured work surface and knead until smooth and elastic, 10 to 12 minutes. Place dough in an oiled bowl in a warm spot, cover with a towel and let rise until doubled, 30 to 45 minutes.

Meanwhile, prepare salsa: Combine tomatoes, fennel, anchovies, red pepper flakes and remaining 2 teaspoons basil. Drizzle with olive oil and sprinkle with salt.

Preheat a grill to medium-high heat. Turn dough out onto a lightly floured surface. Using a sharp knife, divide dough into 4 equal pieces. Roll each piece into a round ball. Roll each ball into a 6- to 7-inch circle; let rest for 10 minutes. Brush each piece with a little oil.

Grill until bread is puffed and slightly charred, turning once, about 5 minutes. Divide ricotta between flatbreads and top with salsa. Return to the grill and heat through, 2 to 3 minutes. Slice into wedges and serve immediately.